







Fractions with roots 
20190206 

From DEBMALYA: 5/√2+√3 –1/√2–√3 Answered by Penny Nom. 





The inverse square law 
20180605 

From Amy:
Question about inverse square law ;
Hi, I'm trying to understand some nuances about this law and
have been reading about it a lot online and trying out some homework
for personal interest (hobby )  not school related.
I understand that the simple formula is ; 1/d^2
I was wondering about what appears to be an oddity to me, that
I came across when I was working with a test example I found at this
link ;
http://www.softschools.com/formulas/physics/inverse_square_law_formula/82/
The problem that caught my interest was this one on that page ;
"1) If a bright flashlight has a light intensity of 15.0 candela at a distance 1.00 m from the lens, what is the intensity of the flashlight 100.0 m from the lens?"
So I have a few different questions about this, but the most important
one is, what does it mean if we replace the "1" in ; 1/d^2 with a different value such as a ratio in the form of a decimal value, so instead we have something like this ;
0.75/d^2
???
Does this ratio represent a curve then?
I am thinking that the "1" in the normal formula represents a straight line
Some of the links I was researching ;
http://wisptools.net/book.php?c=3&s=2
http://www.softschools.com/formulas/physics/inverse_square_law_formula/82/
https://www.ndeed.org/GeneralResources/Formula/RTFormula/InverseSquare/InverseSquareLaw.htm Answered by Penny Nom. 





Subdividing a rectangle into squares 
20180513 

From jeverzyck: A rectangular board is 108cm wide and 156 cm long Equal squares as large as possible
are ruled off this board.Find the size of the square.How many squares are there? Answered by Penny Nom. 





The square root 3 in exponential form 
20180509 

From Paige: how do you write the square root 3 in exponential form Answered by Penny Nom. 





A side of a square 
20180406 

From Angie: I am dyslexic and have problems with spelling and math I'm trying to figure 4.610 Acres Square trying to figure out how many feet or yards of one side if that makes sense to you thank you I'd really appreciate the help Answered by Penny Nom. 





The price of a sheet of metal 
20180402 

From Nydia: What is the formula to calculate the following:
I nee to find out what the sheet price be. The dimensions are 2000x3000 mm into ft they are 78x1181.
The sqft price I have is $22.16. How do I figure out the sheet price from that? Answered by Penny Nom. 





Expand (5x9)(5x+9) 
20180301 

From adil: expand the following:
(5x9)(5x+9) Answered by Penny Nom. 





The perimeter of a square 
20180225 

From Alicia: What's the perimeter of a square with 441cm square Answered by Penny Nom. 





2.5 gallons of liquid, one half an inch deep 
20180221 

From Cain: How many square feet would 2.5 gallons of liquid cover at half an inch deep? Answered by Penny Nom. 





A question about perfect squares 
20180204 

From Jolyn: Find the smallest possible value of a whole number m if 648x m is a perfect square Answered by Penny Nom. 





The square root of 6 is irrational 
20171002 

From John: http://mathcentral.uregina.ca/QQ/database/QQ.09.06/sylvia1.html
In the initial assumption of that proof, root 6 is assumed to be a/b where a and b have no common factors, but why does having a common factor make it irrational? Answered by Penny Nom. 





Squares and rectangles 
20170715 

From Tront: So, there's a general rule that all squares are rectangles but not all rectangles are squares. Im trying to find a term that would describe this relationship. I've found that if all of A is B but not all B is A then I'd say that A is a subset of B, but is there a term that describes the relationship as a whole? I don't want to describe the components, I want to describe the relationship as a whole. Answered by Penny Nom. 





A square peg in a round hole 
20170529 

From bill: bill wants to put a 2 foot square peg into a round hole What must be the circumference of the hole? Answered by Penny Nom. 





A 40 acre square 
20170514 

From Richard: How many feet on each side of 40 acre square ? Answered by Penny Nom. 





1 acre as a 2 foot wide strip of land 
20170425 

From alan: How can one convert 2 acres (a square  area) of land into a strip of land that is 2 feet wide and (?) feet long? Answered by Penny Nom. 





The cost of a piece of sheet metal 
20170414 

From Mohammed: I bought a 2 mm sheet plate of 1.2m × 2.4m in fijian $95. I used 1.95m × 0.4m from that sheet plate. What will be my total cost for the sheet plate I used. It was a mild steel plate. Answered by Penny Nom. 





How much money do I make per sq ft? 
20170328 

From jackie: If I make $12.00 per hour and I cover 750 sq ft in one hour, how much money do I make per sq ft? Answered by Penny Nom. 





An octagon from a square 
20161226 

From Chris: We have a square piece of wood (30 inches x 30 inches) that we need to cut into an octagon. Is there a simple way to figure out where to make the marks/points to cut? I mean like really simple?
Thanks! Answered by Penny Nom. 





1/1cosine(2x)  1/1+ cos(2x) 
20161214 

From Sean: 1/1cosine(2x)  1/1+ cos(2x) Answered by Penny Nom. 





x^2 = 16 
20161212 

From A student: x to the second power = 16
what number solves the equation? Answered by Penny Nom. 





A square inside a circle inside a square 
20161113 

From Jeff: Greetings,
I came across a question from a textbook from years ago. I've been trying to solve it, but am not sure if my approach is correct.
There are 2 squares (1 inner, 1 outer) & 1 circle.
The inner square is the largest square that will fit inside the circle. It has an area of 1 unit.
The circle is the biggest that will fit in the outer square.
What is the area of the outer square? Answered by Penny Nom. 





A search area 
20160813 

From tammy: if your searching an area and you go 300 km from point A and search 380° what or how much area would you search? Answered by Penny Nom. 





A patio slab 
20160427 

From Heaven: Allie used 11.7m^3 of cement to make a square patio. If the thickness of the patio is 15 cm,what is the length of the patio? Answered by Penny Nom. 





A square of side length 4x3 units 
20160420 

From Bryan: Find an expression that represents the area of a square with side length 4x3 Answered by Penny Nom. 





The diagonal of a 10 acre square 
20160411 

From Derrick: I own 100 acre square of land. I want to run from farthest corner of property to farthest corner, Diagonally. How many miles would I have traveled? Answered by Penny Nom. 





The area of a circle and a square 
20160410 

From Richard: I cannot understand why if you have a perimeter say of 4 units as the circumference of
a circle then you reshape it into a square you lose very approximately some 20% of its
volume but the perimeter length stays the same.
Can you please explain this to me as to why the volume decreases. Answered by Penny Nom. 





A square based box and a cylinder 
20160326 

From rajpal: i m trying to calculate an area required to hold 4.4 mln cubic metres of volume.
I used square and I get below result
A box shape that has dimensions 1500 meters (1.5km) by 1500 meters (1.5km) by 2 meters depth has a volume of:
= 4,500,000 cubic meters (4.5 mln cubic meters)
but when I use a cylinder shape, i get below result
A cylindrical shape that has a radius of 850 meters and a depth of 2 meters has a volume of:
= 4,539,600 cubic meters (4.54 mln cubic meters approx)
why is it that the cylinder, though of same depth holds more volume than a square?
kindly clarify. Answered by Penny Nom. 





The perimeter of a square 
20160116 

From dennis: If I have eleven Square Acres, what would the perimeter dimensions be? Answered by Penny Nom. 





The perimeter of a one quarter acre square 
20160115 

From Kerry: If you have a perfect square that is one quarter of an acre what are the length of the sides and how do you arrive at the solution? thank you, Kerry. Answered by Penny Nom. 





The perimeter of a 4 acre square 
20151216 

From samantha: What is the distance in miles or how many laps to make a mile, if one was walking around 4 acres of land which is like a square? Answered by Penny Nom. 





Roof Square footage 
20151111 

From Todd:
Question from Todd:
Good Day.
I have to figure out the square footage of a quonset style roof that's not playing by the rules The building dimensions (rectangular) are 63'x135' the height of the roof is 9.25'. It not an entire Quonset, It's that style of roof,(curved). There are concrete block walls 10' up to the metal roof.
Thank you!
Todd Answered by Harley Weston. 





Square roots 
20150921 

From mariana: I have read various articles on how to find the square root of irrational numbers and every article out there seems to be very confusing.
i read you answer to LUKOW about irrational numbers and i am still quite confused. Say i want to find the square root of 326. i know that it is between 18 and 19 because 18 is the square root of 324 and 19 is the square root of 361 im just very confused about the rest of the process. Please help! ( if possible i would appreciate two examples. thanks) Answered by Penny Nom. 





A procedure for finding a square root 
20150827 

From Tracey: Is there a method/process to determine the square root of a large number?
For example, Tiananmen Square's area is 396 900m sq., what is the side length?
Thank you,
Tracey Answered by Harley Weston. 





Why is the area of square not conserved when it changes to a rhombus? 
20150628 

From shubham: Why is the area of square not conserved when it changes to a rhombus, both have equal sides still rhombus have less area than square.?? Answered by Penny Nom. 





2^48  1 
20150613 

From Soham: The number 2^481 is divisible by two numbers between 60 and 70. The sum of
the two numbers is? Answered by Penny Nom. 





A square and a rectangle 
20150501 

From nick: why is the area of a square of a given circumference greater than the area of a rectangle with the same circumference ? Answered by Penny Nom. 





A circle inscribed in a square 
20150419 

From michael: A circle is drawn in a square PQRS. If the total area of the shaded portion of the square is 42 cm square, calculate the radius of the circle Answered by Penny Nom. 





An 8 pointed star inscribed in a circle 
20150410 

From Kermit: How do you find the area of the star that is formed by two squares and surrounded by a circle. The only given information is that the radius of the circle is 10. Answered by Penny Nom. 





Is a rhombus a square? 
20150324 

From Justin: Is a rhombus a square? Answered by Penny Nom. 





The center and radius of a circle 
20150206 

From ariana: I need to find the center and the radius of this circle. I don't know how to put 9/2
than square it into a fraction.
x^2 + 2x + y^2 +9y=5 Answered by Penny Nom. 





Is a square a trapezoid? 
20150126 

From Katie: Can a trapezoid sometimes be a square? Answered by Penny Nom. 





A line segment of length root 5 
20141215 

From angela: On the dot grid below, draw and label a line segment with length square root 5
the dot grid is 8 by 10 Answered by Penny Nom. 





A truncated, squarebased pyramid 
20141123 

From Hannah: A designer vase has the shape of a truncated, squarebased pyramid. The base of the vase is a square with a side length of 15 cm. The area of the square opening is 70.56 cm2. Each of the four sides is a trapezium with slant sides 9 cm long. Find (to the nearest square centimetre) the total surface
area of the vase. Answered by Penny Nom. 





How many square feet in 10 gallons of liquid at 1/4 in thick? 
20141114 

From Rich: How many square feet in 10 gallons of liquid at 1/4 in thick Answered by Penny Nom. 





(x3)^2(x+3)^2 
20141113 

From Bernice: (x3)^2(x+3)^2 Answered by Penny Nom. 





What is 3 squared? 
20141112 

From Christine: On a math test, it said "What is 3 squared?" It did NOT say "What's is (3)squared"
The teacher's explanation is that if there are no brackets or parenthesis, you ALWAYS square the number first then do the negative, so the answer should be 9, but I can't find anywhere that confirms this.
Help please. Answered by Robert Dawson. 





A truncated squarebased pyramid 
20141022 

From Beth: How do you find the height of the original squarebased pyramid when given the sides (12cm) of the base and height (6cm) of the truncated pyramid, as well as the sides (3cm) of the base of the chopped off top (chopped off parallel to the base)? Answered by Penny Nom. 





How do you convert square mm to square cm? 
20140813 

From David: How do you convert square mm to square cm? Answered by Tyler Wood. 





Covering a 12 inch by 12 inch square hole 
20140702 

From Patricia: I am putting in a new bathroom fan. I am wondering if a new light with a 15 inch diameter will cover the existing square hole which is 12 by 12 inches? If the existing hole is 11 1/2 by 11 1/2 inches?
Also, if the 15 inch diameter does not cover the 12 by 12 hole, what size diameter would?
Thank you. Answered by Penny Nom. 





A circle a square and a rectngle 
20140512 

From mazhar: suppose the length and breadth of the rectangle are 5 cm and 10 cm respectively and M is a point along the corner of the circle. what is the radius of the circle?(diagram is given..but i didn't mention it..actually the diagram looks like a circle inscribed in a square and the right bottom corner one rectangle will be given ,it is touches to circle at a point M that I've already mentioned and the dimensions of that rectangle also I've mentioned) please help me out.. Answered by Penny Nom. 





A square garden 
20140209 

From reeta: Inside a square garden of side 158m, a road 4m wide is built all around. What is the area of the remaining part of the Answered by Penny Nom. 





A square frame 
20140101 

From steve: using 6" wide boards how many inches would each of 4 boards equal in length need to be to produce a square with an inside perimeter of 84 inches on a side? what is the exterior perimeter? There is to be 45 degree cuts at each end of each board.
What formula is used to make this calculation? Answered by Harley Weston. 





Can 100r^281z^2 be factored? 
20131208 

From Rosa: Can 100r^281z^2 be factored? Answered by Penny Nom. 





Fractions and square roots 
20131204 

From arionne: How do you solve a square root with improper fractions like 121 over 49 Answered by Penny Nom. 





A square inscribed in a circle 
20131014 

From Jenn: Hello! I am about to buy a 7'9" round rug, but I want to have it cut down into a square. What's the largest square I can obtain from this? Thank you! Answered by Penny Nom. 





The perimeter of a 1.4 acre square 
20130829 

From Destini: I cannot figure out what the perimeter for 1.4 acres of land
in the shape of a square. I have tried and tried and eventually
tried to use a calculator and I still can't figure it out. Can you
help me? Thanks!
Destini Answered by Penny Nom. 





Squares and cubes 
20130802 

From Sandra: What whole number equals 25 when it is squared and 125 when it is cubed? Answered by Penny Nom. 





The square footage of a 17 inch by 17 inch tile 
20130518 

From Leroy: How do I calculate the square footage of a 17inch by 17 inch tile Answered by Penny Nom. 





(4 4cos^4 x)/(sin^2 x) 
20130518 

From Agnes: How I can solve this question :
Simplify (4 4cos^4 x)/(sin^2 x) and write in terms of sin x Answered by Penny Nom. 





We have 2 teams of 6 couples each that play 6 games 
20130125 

From Denise: We put together a game night where we have 2 teams of 6 couples each that play 6 games. We haven't been able to figure out an arrangement that allows each couple to play each game with a different couple from the opposite team (i.e. Team A couples play every game with a different couple from Team B). Is this possible? It works with 2 teams of 5 couples each. Answered by Chris Fisher. 





Milling round stock to square stock 
20121217 

From Bryan: Question from Bryan:
I want to know what the smallest diameter round is that will make a 31/4" square? Is there a formula for that? I am milling round stock into square.
Thank you. Answered by Harley Weston. 





Difference of squares 
20121119 

From Qelibar: Please factorise x^2y^2  4 Answered by Penny Nom. 





The square of any odd number, decreased by 1, is divisible by 8 
20121116 

From bailey: Prove that the square of any odd number, decreased by 1, is divisible by 8 Answered by Penny Nom. 





Square root 
20121027 

From Ashley: what does square root means Answered by Penny Nom. 





3 acres 
20121016 

From Katy: If 3 acres of land were a complete square, how many feet would be on each side? Answered by Penny Nom. 





0.687 acres in square feet. 
20120718 

From Roy: The land parcel I am looking at says Acreage .687 how do I determine square feet? Answered by Robert Dawson. 





Two equations involving fractions 
20120612 

From Fatima: Hi ,teacher gave two question to my daughter as follows
Solve 2/x+3=(1/xx9)(1/x3)and
Solve (4/x2)(x/x+2)=16/xx4
Please help me
Thanks & regards fatima Answered by Penny Nom. 





Two ways that a deck is square 
20120430 

From romel: describe two ways that a deck is square Answered by Penny Nom. 





The price per square inch of a pizza 
20120317 

From jordan: pizzaz pizza sells a small pizza for $10.99.it has a diameter 10 inches.what is th price per square inch ? Answered by Penny Nom. 





Square numbers 
20120317 

From david: How many square numbers are there between 0 to 100? Answered by Penny Nom. 





A road around a garden 
20120207 

From Manu: Inside a square garden of side 158m, a road 4m wide is built all around. What is the area of the remaining part of the garden? Answered by Penny Nom. 





A quartic polynomial that is a perfect square 
20120205 

From archit: If P(x)=x^4+ax^3+bx^28x+1 is a perfect square then (a+b)=? Answered by Penny Nom. 





Sum and difference of squares 
20111231 

From Anne: Se x e y são números reais distintos, então:
a) (x^2 + y^2) / (x  y) = x + y
b) (x^2 + y^2) / (x  y) = x  y
c) (x^2  y^2) / (x  y) = x + y
d) (x^2  y^2) / (x  y) = x  y
e) Nenhuma das alternativas anteriores é verdadeira. Answered by Harley Weston. 





Triangular numbers that are square 
20111227 

From Luke: The “TnS” is a positive integer which is both Triangular number
and Square number. For example, 36 is a “TnS” number
since 36=1+2+3+4+5+6+7+8 (Triangular number)
and 36=6x6 (Square number).
What is the next “TnS” which is greater than 36? Answered by Penny Nom. 





Squares and triangles 
20111206 

From Liaqath: You have squares and triangles.
Altogether there are 33 sides.
How many squares do you have?
How many triangles do you have? Answered by Penny Nom. 





The square root of z=3+4i 
20111027 

From dianah: how to find the square roots of complex number, z=3+4i Answered by Robert Dawson. 





U(n+1) = 2Un + 1 
20110522 

From Cillian: In a certain sequence, to get from one term to the other you multiply by 2 and add 1, i.e. This is a difference equation of form: U(n+1) = 2Un + 1. prove that there is a maximum of 2 perfect squares in this sequence Answered by Claude Tardif. 





A rational number 
20110517 

From owais: according to definition of irrational number "a number which cannot be
expressed in p/q form is called irrational number"
square root of 2 is a irrational number but if i round off the digit correct
to two decimal places so it becomes 1.41 and we can easily convert
into p/q form so it is a rational number ??? Answered by Penny Nom. 





Two whole numbers 
20110511 

From yolanda: The sum of two whole numbers is 12.If the sum of the squares of those numbers is 74,what are the two numbers? Answered by Penny Nom. 





A circle in a square in a circle in a square 
20110329 

From George: A circle within a square which is inside
a larger circle which is also within a square.
(a circle in a square inside a circle in a square)
Equation of the smaller circle is: x ^ 2 x y ^ 2 = 25.
What are the dimensions of the larger square?
Been 40 years, trying to help my son. Answered by Penny Nom. 





(3x+4y)^2  (2xy)^2 
20110316 

From Taiwo: pls could some one help me with this question? thanks as lot
factorize:
(3x+4y)^2  (2xy)^2 Answered by Penny Nom. 





A circle inside a square 
20101231 

From Jenn: A circle of a diameter of 2 is drawn inside a square of 4. The circle's center is at the center of the square. To the nearest tenth, what is the perimeter of the area of the square, not including the circle inside. Answered by Penny Nom. 





A rectangular piece of plywood 
20101130 

From Austin: A rectangular piece of plywood is trimmed to make it square by cutting a 4cm strip off the top and a 2cm strip off one side. If the area of the original piece is 74cm2 greater than the area of the square, find the dimensions of the rectangle. Answered by Penny Nom. 





I have a sign size regulation I have to meet. 
20101026 

From Scott: I have a sign size regulation I have to meet. The size is .6 meters squared. at first look this would be 2 ft x 2 ft.
I believe it would be larger then that. Can you confirm what the size would be in inches please. Answered by Penny Nom. 





Tiles on a bedroom floor 
20101007 

From Rochelle: John's bedroom floor is square in shape. He used 625 tiles, with a side length of 200 mm, to tile the whole floor.
Calculate the area and dimensions of the bedroom Answered by Penny Nom. 





What is 2^2? 
20100825 

From alex: I know that (2)^2 is 4 but what is 2^2? Answered by Robert Dawson and Penny Nom. 





A square field has an area of 289 meter squared 
20100802 

From daniel: a square field has an area of 289 meter squared. How do you calculate the dimensions Answered by Stephen La Rocque and Penny Nom. 





The area of a 4 sided region 
20100714 

From Cliff: If I wanted to know the square footage of an area that has four different sides and only had the length of one side and the angles at the ends of that length; could the other lengths be found if I wanted to have a total of 130,680 square feet? Answered by Robert Dawson and Tyler Wood. 





Four circles in a square 
20100604 

From Daniela: four circles are drawn in a square such that the circles are tangent to each other as shown. find the area of the shaded region. It the goes on to show a diagram with a square and four circles drawn in it. The length of a side of the square is 24. Please help me! Answered by Penny Nom. 





A square pyramid 
20100526 

From Georgia:
Question from Georgia, a student:
I have been given the following question in a maths assingment, and have so far been unable to answer it.
To begin, i am required to draw a square pyramid as follows:
1. draw a 3 dimensional diagram of a square based pyramid
2. label the square base as ABCD, call the vertex H.
3. Mark in E and F the midpoints of AD and BC respectively and O is the midpoint of EF
Note: this therefore makes FO = FC
this i was fine with, it was the following question that stumped me.
1. if the height of the pyramid is 280m, what is the length of the base?
Thanks, Georgia Answered by Chris Fisher. 





A square inscribed in a circle 
20100525 

From Middle: what is the perimeter of a square inscribed in a circle of radius 5.0 inches? Answered by Penny Nom. 





How many sq. ft in 2 1/2 ft x 2 1/2 ft? 
20100516 

From jim: how many sq. ft in 2 1/2 ft x 2 1/2 ft Answered by Penny Nom. 





Tiles 
20100425 

From Pat: how many 6 inch tiles will I need to purchase for an area that is currently covered with 351 4 inch by 4 inch tiles.
Each box of 6 inch tiles states it contains 16 pieces and covers 4 square feet. Answered by Penny Nom. 





A 12 foot by 12 foot room 
20100420 

From Dominique: The room is 12ft by 12ft. How many yards must be purchased for the carpet? Answered by Penny Nom. 





Two problems 
20100413 

From Dorothy: 1. Explain why the number 123, 456, 789, 101, 112 cannot be a perfect square. (Hint: What is the units digit?)
2. A substance doubles in volume every minute. At 9:00A.M., a small amount is placed in a container. At 10:00A.M., the container is just full. At what time was the container oneeighth full? Answered by Robert Dawson. 





A roll of polythene 
20100404 

From Mary: I have an area of 54square metres to cover how many rolls of 2m x 50m polythene do I need Answered by Penny Nom. 





The side length of a square 
20100308 

From tara: am trying to help my brother's daughter in maths, tomorrow she has maths exam
1. Area of sq. picture is 441 sq.cm what is the length of its side. Answered by Penny Nom. 





A related rates problem 
20100303 

From Amanda: A circle is inscribed in a square. The circumference of the circle is increasing at a rate of 6 inches per second. As the circle expands, the square expands to maintain the tangency. Determine the rate at which the area of the region between the circle and square is changing at the moment when the cricle has an area of 25(pi) square inches. Answered by Penny Nom. 





A perfect square 
20100220 

From george: can this number 400....006 be a perfect square . how to solve problems like this. Answered by Chris Fisher and Tyler Wood. 





The perimeter of a square 
20100218 

From richard: My question is: In yards what is the perimeter of a piece
of land totaling 6.2 acres. This land is a perfect square. Answered by Melanie Tyrer. 





A magic square 
20100218 

From Mika: place the integers from 5 to +10 in the magic square so that the total of each row, column, and diagonal is 10. Answered by Tyler Wood. 





Square poles 
20100216 

From Steve: If 1 pole=16.5', and you have an area that is 146 sq. poles, how many sqaure feet would you have?
I calculate that to be 146(16.5)X146(16.5)=5,803,281 sq. feet Is that correct? I am told I need to divide by 146, which makes the answer 39,748. I do not understand why I need to divide by 146.... Answered by Penny Nom. 





A square corner 
20100211 

From Trevor: I am building a new house and wish to set it out on site with the use of
profile boards and string. I want to be certain it is correct in terms of
squareness. I have a vague idea that the square on the hypotenuse should
be equal to the sum of the squares of the other two sides.
I get a little lost here and need some help. The building is a rectangle
measuring 40x30 feet to exterior brickwork. I guess that the length
of the hypotenuse should be exactly the square root of the combined
squares of the two sides.
Using the above measurements could you give me calculations from nuts
to soup as to the correct length of the diagonal. And what adjustments
are needed if everthing is not in accord.
Trevor. Answered by Robert Dawson. 





Bending a wire to form shapes 
20100204 

From Geraldine: a wire bent into the shape of a square encloses an area of 25cm squared. then the same wire is cut and bent into two identical circles. what is the radius of one of the circles round to the nearest hundred Answered by Penny Nom. 





Is it a square? 
20100129 

From Manick: I have a question. how to find whether a given integer is a perfect square or not? Answered by Robert Dawson. 





Area in square meters 
20100120 

From Carla: A football field is 120 yd long and 50 yd wide. What is the area of the football field, in square meters? Answered by Penny Nom. 





The square root of a large number 
20100119 

From darlene: I understand the simple process, like 12 is the root to 144 but what happens when the number is 42563. Without a calculator how does a person figure this out during a timed test? Answered by Robert Dawson. 





Cutting a square into four shapes 
20100105 

From Tracy: A square with a side of 4 ft needs to be cut into four shapes with the same area. can you find six different was to cut the square? Answered by Robert Dawson. 





Figure out the square root of something 
20091220 

From eric: is there an ez equation to figure out the square root of something? Answered by Harley Weston. 





A concrete slab 
20091210 

From Mark: there are 30 cubic yards of concrete, how many feet will it cover with a 4" slab? Answered by Penny Nom. 





(9  x^2)/(x  3) 
20091204 

From Sandy: 9x^2/x3
I need to know how to solve this.
Thanks Answered by Penny Nom. 





Rationals 
20091030 

From Jawsh: I don't quite understand the whole idea of rationals.
If you have 3Squareroot 49. Is that equal to 3Squareroot 7^2?
Can you break it down with an example for me please. Answered by Robert Dawson. 





Forming a square 
20091021 

From christianah: Two parallel lines have the equations y=x+4 and y=x2.Two additional lines are drawn to form a square.What is the side length of the square?Write possible equations for the additional lines.Explain and justify your reasoning. Answered by Penny Nom. 





Completing the square 
20091002 

From christopher: how do i find the factors of x^2+3x+2 by completing the square ? Answered by Robert Dawson. 





Grams per square meter 
20090930 

From MANISH: how to calculate gsm given kg of 144 sheets and size in inches
example 28" x 22" & 16.3 kgs = ?gsm (of 144 sheets) Answered by Penny Nom. 





Cubes and squares 
20090916 

From Stanley: What is a three consecutive digit number like 5,6,7 , which is two less than a cube and two more than a square? Answered by Robert Dawson. 





The inverse of F(x)=x^26x+13, for x>3 
20090726 

From Juan: The function F is given by F(x)=x^26x+13, for x>3.
A. Write F(x) in the form (xa)^2+b
B.Find the inverse function F^1
C.State the domain of F^1 Answered by Penny Nom. 





Inequalities Proof 
20090724 

From ABOU: good morning.......a b c are real positive no zero......proof that
sq root(2a/(a+b))+sq root(2b/(b+c))+sq root(2c/(c+a))inferior or equal 3
thank you Answered by Janice Cotcher. 





A degreaser for a fish tank 
20090723 

From charlie: I have a tank that is 10 feet in diameter that I want to put floating degreaser in.The rate for the degreaser is 1/2 gallon per square foot of surface water.How do I figure out how many gallons I need? Answered by Penny Nom. 





Completing the square 
20090616 

From rebecca: Find the roots of the equation by Completing the square. Express your answer in exact form and in decimal form to 2 decimal places.
a) x(squared)+10x+23
b)3y(squared)+12y+3 Answered by Stephen La Rocque. 





Area and perimeter 
20090507 

From Kelly: Why do objects w/ the same exterior linear feet have different interior sq ft? I.e. a 25x25 room has 625 sqft while a 20x30 room has only 600 sqft? I can visualize that by cutting and moving parts of the rectangle, you loose a 5x5 section, but I just can't get my head around why. Answered by Robert Dawson and Stephen La Rocque. 





5^2= 25 
20090506 

From tracy: show how to perform this calculation and why
5^2= 25 Answered by Robert Dawson. 





Completing the square 
20090427 

From Daniel: I tried following an example of yours but I still couldn't figure it out.
Here is my question,
2x^2  6x + 1 = 0.
Any help would be greatly appreciated. Answered by Stephen La Rocque. 





How many rectangles are in a square prism? 
20090409 

From Lorenya: How many rectangles are in a square prism? Answered by Robert Dawson. 





Pounds per square foot 
20090404 

From kevin: Ineed to know the pds per sq ft of a machine that weighs 1,550 pds and measures 78.5 inches long x 32 inches wide. Answered by Harley Weston. 





Square prisms and pyramids 
20090403 

From Sheyna: What are the differences between a square prism and a pyramid?
 Sheyna Answered by Penny Nom. 





Square feet and acres 
20090331 

From ROZELL: how much land is 660'x400' also how many feet in one hundred acres Answered by Harley Weston. 





More on the square root of 0.75 
20090330 

From Blaine: I read your response to How is the square root of 3/4 is greater than 3/4?
What I'm hoping for is a way for my students to use their own experience and number intuition to be able to make sense of the issue. As soon as my kids see "if y is this and x is this then..." their little eyes glaze over. Unfortunately, I can't come up with a way myself. Thank you for your help. Answered by Penny Nom and stephen La Rocque. 





Simplify the square root of 125 x^2 
20090227 

From Ashley: √125x²
How do you simplify this equation assuming that variables can represent any real number? Answered by Robert Dawson. 





A goat in a square paddock 
20090210 

From lachlan: A farmer uses a rope to tether a goat to a pole at the corner of a square paddock. The length of one side of the square is 24m.
a) If the length of the rope is 12m,what % of the paddock can the goat reach? is the answer 19.62 %?
b) If the farmer wants the goat to be able to graze exactly half the area of the paddock, what length must the rope be? Answered by Penny Nom. 





The units digit is 5 
20090202 

From Ray: the number that when squared the units digit is 5 Answered by Penny Nom. 





The resulting number is the square of an integer 
20090130 

From Randy: A positive integer n is chosen. Then the product n ( n + 1 )
is computed and two digits are appended to the end of the product. The
resulting number is the square of an integer.
Show that it is always possible to complete the process above or give a
positive integer n for which the process cannot be completed. Answered by Chris Fisher and Claude Tardif. 





An octagonal carpet 
20090124 

From Larry: I am cutting a piece of carpet that is 9 feet x 9 feet and need to cut it into an octagon. How far do I cut from the corner of the square. thank you for any help. Answered by Harley Weston. 





Factor x^2  y^2 
20090120 

From Shell: complete Factor: x^2y^2 Answered by Penny Nom. 





Square footage 
20090120 

From david: 15 3 5/8 x 18 7" Answered by Penny Nom. 





The square root of 164 
20081231 

From Melissa: How do you simplify the square root of 164? Answered by Stephen La Rocque. 





Square yards of dirt cover 
20081208 

From Phillip: How many square yards will 600 cubic yards of dirt cover, at a depth of 4 inches? Answered by Harley Weston. 





A circular plaque in a square box 
20081128 

From kmart: A square box has a diagonal of length 640cm.It is to contain a circular wall plaque. What is the
approximate diameter of the largest wall plaque that can be placed in the box? Answered by Penny Nom. 





Factor 9x^2 + 6x + 4 
20081121 

From Jonah: how can i solve this by factoring: 9x^2 + 6x + 4 Answered by Harley Weston. 





Four circles in a square 
20081119 

From Anthony: I have a square where one side measures 10cm and within that square
There are four equal quarter circles. Each quarter circles starts in a
different corner of the square and I am trying to find area inside the
overlap on the quarter circles. Answered by Janice Cotcher, Chris Fisher and Penny Nom. 





Factoring 
20081119 

From Neji: How do you factor (yz) (y+z) (y^4+y^2z^2+z^4) and get (y+z)(y^2yz+z^2) (yz) (y^2+yz+z^2) as the answer? Answered by Harley Weston. 





The cost of a steel plate 
20081105 

From Tammie: What is the formula to calculate the following:
I have a plate of steel that is 1/4" x 48" x 192" at a price of $15.23 per square foot
What is the formula to calculate the cost if I only use 1/4" x 471/4" x 681/8" of that steel plate? Answered by Penny Nom. 





The area of a square 
20081020 

From Danny: Is it possible to use a circumference measurement to find the area of a square when all 4 corners have a 1.75" radius? Answered by Harley Weston. 





What is the square of 20? 
20081019 

From john: what is the square of 20? Answered by Penny Nom. 





The area of a rug 
20081016 

From Natcha: How can I convert the Carpet Roll Size to Square Meters.
I have one Roll of carpet, (Quality is 2300 g/m2; 7 pitch/in, 9 rows/in; width: 2m) with dimension 0.5 m width and 4 m length. I needed to know that quantity of that Roll in Square Meters. Answered by Penny Nom. 





Solving an Equation with a Square Root 
20081005 

From Jonathan: the square root of 3x+18 = x
3x+18 are within the square root Answered by Victoria West. 





z(z+1)x(x+1) / zx 
20080930 

From sylvia: z(z+1)x(x+1) / zx
HOW DO I SIMPLIFY THIS Answered by Penny Nom. 





a(a+1)  b(b+1) 
20080930 

From Shaun: I need to factor (ab) out of the following: a(a+1)  b(b+1). I know it is simple but I cannot remember how. Answered by Penny Nom. 





The length of one side of a square 
20080928 

From Mela: The area of a square is 841cm².
What is the length of one side of the square?
What is its perimeter? Answered by Penny Nom. 





144 square inches 
20080927 

From mike: how much cm is in 144 square inches? Answered by Penny Nom. 





How many miles of track? 
20080827 

From Stephanie: I have a 50 ac tract of Railroad I need to know approx how many miles of tr=
ack would be included in 50 ac Answered by Penny Nom. 





The square root of a fraction 
20080824 

From Lauren: How do you solve square roots of fractions? Does the format change if it is either a proper or an improper fraction?
Ex. the square root of 1/4 or the square roots of 80/25 Answered by Penny Nom. 





Simplifying Algebraic Expressions 
20080822 

From Jacky: x^2y^2+4x+4y Answered by Penny Nom. 





A square with diagonal 200 metres 
20080820 

From kelvin: find the are and perimeter of a square with diagonal of 200 meters? Answered by Penny Nom. 





Factoring x^2 + 729 
20080819 

From peter: hello I,am having trouble factorising a polynomial into polynomial factors
with real coefficients please can you help the polynomial is x^2+729 Answered by Harley Weston. 





Is zero a perfect square? 
20080814 

From peter: is zero a perfect square? Answered by Penny Nom. 





Square miles 
20080806 

From Koni: I'm trying to figure out the distance our buses travel throughout our district to pick up students for school. How do you figure square miles?
If our district measures 6 1/2 miles wide and 2 3/4 miles deep, what is our total square miles? Answered by Penny Nom. 





Finding Angles in a Pyramid 
20080730 

From Carla: A pyramid has its vertex directly above the centre of its square base. The edges of the base
are each 8cm, and the vertical height is 10cm. Find the angle between the slant face and the base,
and the angle between the slant edge and the base. Answered by Janice Cotcher. 





The length of a side of a square 
20080727 

From FRANK: WHAT IS THE LENGTH OF ONE SIDE OF A SQUARE WITH A DIAGONAL OF LENGTH 2 TO THE HALF POWER Answered by Stephen La Rocque. 





A square is inscribed within a square 
20080719 

From Shirley: A square is inscribed within a square that has a side the measures 16
centimeters. The vertices of the smaller square are located at the midpoints
of the sides of the larger square. What is the area of the larger square, area of
a smaller square, the probability that a point chosen at random is in the
shaded are? Express the answer as a simplified fraction. Answered by Penny Nom. 





A four sided lot 
20080709 

From michelle: the front is 65.29
left side 162.26
the back 155.00
right side 101.01
right angle=50.00
left angle= 153.30 Answered by Harley Weston. 





What is the largest perfect square factor of 1512? 
20080702 

From peter: What is the largest perfect square factor of 1512? Answered by Penny Nom. 





The square root of (18*n*34) 
20080701 

From Peter: What is the least possible positive integervalue of n such that square root(18*n*34) is an integer? Answered by Penny Nom. 





Acres and square miles 
20080625 

From Jill: how many miles are in 417 acres Answered by Penny Nom. 





A circle inscribed in a square acre 
20080619 

From Scott: Q'm trying to find out the sq footage of the corners of an acre. If an acre is 43,560 sq and if I have this right the surface area of the circumference is 1040 ft. what is the combined square footage of the 4 corners? Or the percentage the original acre? Answered by Harley Weston. 





The length of a piece of fabric 
20080531 

From Jeanie: How do I convert square yards to linear yards? I know the width of the fabric is 54" wide. I am at a loss of what the formula is to figure this out; please help! Thanks! Answered by Penny Nom. 





A triangle and a square 
20080524 

From s: how to construct a triangle whose area is equal to the area of a given square? Answered by Penny Nom. 





An octagonal prism 
20080427 

From Melanie: My son is identifying geometric shapes in the real world? We are stuck on octagonal prism, rectangular prism and square prism. Can you help me out with some examples. Thanks Answered by Penny Nom. 





The sum of the squares of the fibonacci numbers 
20080427 

From Thomas: Hey I have a question for a research topic that our teacher set us, It is regarding the sum of the squares of the fibonacci numbers.
The question says describe the pattern that exists and write a general formula that describes the relationship illustrated above.
I can see the pattern that is occurring but i cannot put this into a general formula.
Any help would be appreciated.
Thanks Tom Answered by Victoria West. 





How is the square root of 3/4 is greater than 3/4? 
20080422 

From Serena: How is the square root of 3/4 is greater than 3/4? Answered by Penny Nom. 





Why can't a square be twice another square? 
20080420 

From kim: why can't a square number double another one Answered by Penny Nom. 





WHY 144 where does this figure come from 
20080419 

From Sean: Why do you use the number 144 to divide
EG. length of timber 2 inches x 8 inches x 14 foot = 1.5 cubic feet
Calculation is 2x8x14 =224 divide by 144 = 1.5 WHY 144 where does this figure come from Answered by Leeanne Boehm. 





A rectangle word problem 
20080410 

From Nick: A rectangle is twice as long as it is wide. If the length and width are both increased by 5cm, the resulting rectangle has an area of 50cm^2. Find the dimensions of the original. Answered by Penny Nom. 





Complete the square 
20080409 

From jessica: can you check my answer please thanks
f(x)=2x^24x+5
I got 2(x+2)^23 for when it asked to simplfy it to standard form of a quadratic
equation Answered by Stephen La Rocque. 





Complete the square 
20080409 

From jessica: Use the technique of completing the square to put f(x)= 2x^24x+5
in the form f F(x)= a(xh)^2+k were h,k=vertex of the parabola.
identify the coordinate (h,k)of the maximum or minimum point
of the associated parabola Answered by Penny Nom. 





A square garden of tulips 
20080408 

From Vincent: Each year Brandon plants tulip bulbs in a square flower bed. This year Brandon's flower bed has 29 more bulbs than it had last year. If the flower bed is still square how many tulip bulbs are in it this year? Answered by Penny Nom. 





100 yards of cloth 
20080404 

From Leroy: (100 yards of cloth 48 inches = how many square yards) Answered by Penny Nom. 





The square root of 21 between what two numbers? 
20080403 

From Danielle: The square root of 21 between what two numbers? Answered by Penny Nom. 





Ounces and grams 
20080402 

From Rakesh: 7.2 oz per sq. yard equals ? __ grams per sq. meter
How I can measure the weight of a Jeans fabric (in oz)? And what is the rellation between grams and oz? Answered by Penny Nom. 





Square feet and square yards 
20080401 

From Victor: 6200 sq. ft.into yards Answered by Penny Nom. 





Cost per square metre 
20080331 

From sandy: if something measures 7m x 3.6m with a depth of 1  1.5m and the total cost is 52 500.00, what is the cost per square metre Answered by Penny Nom. 





The length of a side of a square 
20080312 

From laura: if i had a square of 2.3 square meters what would its radius be?(in centimeters please) Answered by Penny Nom. 





A circle and a square 
20080312 

From mae: what are the formulas on getting the area of the square outside an inscribed circular region? Answered by Penny Nom. 





Completing the square 
20080311 

From Ryan: solve for x by completing the squares,
x^2+4x8=0 Answered by Stephen La Rocque. 





Is every rectangle a square? 
20080304 

From Odette: if every square is a rectangle, is every rectangle aslo a square? Answered by Penny Nom. 





Is a square a rectangle? 
20080229 

From Jaime: Is a square a rectangle? Answered by Penny Nom. 





A new carpet 
20080228 

From Rhiannon: The Gatlins are buying a new carpet for their house. They need about
1,175 square feet of carpet. The carpet they buy is sold by the square yard.
Estimate the number of square yards of carpet they need. Do I use the
formula to find the volume or are? Answered by Penny Nom. 





10 squares drawn one inside another 
20080225 

From Rajesh: There are 10 squares drawn one inside another.The diagonal of the inneremost square is 20 units. if the distance b/w the corresponding corners of any two successive squares is 1 unit, find the diffrence between the areas of the eigth and seventh square counting from the innermost Answered by Stephen La Rocque. 





5x^2  45 
20080211 

From Tiana: factor:
5x^2  45 Answered by Stephen La Rocque. 





A square and an equilateral triangle 
20080210 

From Emily: A square pen and a pen shaped like an equilateral triangle have equal perimeters. Find the length of the sides of each pen if the sides of the triangular pen are fifteen less than twice a side of the square pen. Answered by Stephen La Rocque. 





Cost per square yard 
20080205 

From Terry: MY cost for seed is $325.00 per acre...i want to bring that down to $ per sqyard. Whats the formula? Answered by Penny Nom. 





Determine the number of square inches for one piece of pie 
20080131 

From Annie: Ok i'm so lost it ain't even funny! HELP! Here's the question: A pie has a
radius of 7 inches and can be divided into 8 equal pieces. Determine the
number of square inches for one piece of pie. Explain your answer. Answered by Penny Nom. 





The acre measurement of a property 
20080130 

From Kim: I would like to know the acre measurement of a property that is 673.68 feet by 820.76 feet. Answered by Penny Nom. 





Inscribed square in a triangle 
20080127 

From Adrian: Consider a rightangled triangle PQR, where QR is the base and PQ is the height.
QR=4cm and PQ=3cm. A square is inscribed in this triangle.Determine the length
of one side of the square. Answered by Stephen La Rocque. 





0.18 of an acre 
20080109 

From susan: what is the square footage of .18 of an acre of land? Answered by Penny Nom. 





The area of a piece of property 
20080105 

From Greg: I need to know the area of a six sided piece of property. I sent a map by regular mail. Answered by Harley Weston. 





Simplifying square roots 
20071219 

From Ciara: How would you calculate 2 to the square root of 8 plus 4 to the square root of 2 minus 5 to the square root of 2? Answered by Stephen La Rocque. 





For how many positive integers n is n^2 + 96 is a perfect square? 
20071218 

From Rajesh: For how many positive integers n is n^2 + 96 is a perfect square ? Answered by Penny Nom. 





Finding all the angles 
20071213 

From Rajesh: An eqilateral triangle is drawn in a square with one of the side as its base and draw the lines from the other angular sides such that there are four triangles
formed inside the square which includes the equilateral triangle.I want to know all the angles of all the triangles formed inside the square. Answered by Stephen La Rocque and Penny Nom. 





Square yards 
20071130 

From Chad: I need to convert 4,599 Cubic Yards to Square yards. The thickness is 10 inches. Is there a formula for this conversion.
Thanks, Answered by Penny Nom. 





The square footage of a property 
20071130 

From Warren: The west property line is 240' long with a 90degree angle to the south property line.
The south property line is 493' long with a 90degree angle to the east property line.
The east boundary is 165' long.
The length of the north property line is not known but it is a straight line from the north end of the east property line to the north end of the west property line.
Could you please tell me the total square feet and how many acres?
And how you calculated the answer Answered by Penny Nom. 





More on completing the square 
20071129 

From June: x^2  6x = 16 I found you already had this question but the answer you gave did not help me to explain how to answer the problem for my daughter. I do not understand how to complete the square for this paticular question and the example you showed did not help. I would appreciate any further help you could give me. Answered by Penny Nom. 





A square near 522 
20071128 

From ali: What a way to know the smallest number could blow number 522 to become fully square Answered by Penny Nom. 





Completing the square 
20071126 

From Julie: x^2  6x = 16 Please, Help I am stuck on this math problem. I need to solve by completing the square. I need the steps of solving the problem and the answer, Please. Answered by Penny Nom. 





A 4 by 4 magic square 
20071121 

From sue: This is for my 10 year old nephew. His math question is: he has a 4X 4 magic square. The top squares are from left to right: 359,356,353,366. He says that columns are supposed to equal 796. We can't figure it out and would really appreciate any help we could get. Answered by Penny Nom. 





Expand (a^4  b^4) 
20071117 

From Saif: how would you expand (a^4  b^4) ??? Answered by Stephen La Rocque and Victoria West. 





Completing the square 
20071101 

From Mark: An architect is designing a museum entranceway in the shape of a parabolic arch represented by the equation y = x2 + 20x, where 0 x 20 and all dimensions are expressed in feet. Determine the maximum height, in feet, of the arch. Answered by Stephen La Rocque. 





A circle is inscribed in a square 
20071028 

From Carolyn: A circle is inscribed in a square. What percentage of the are of the square is inside the circle. Answered by Victoria West. 





Given a six by six square, how rectangles are there in the square? 
20071024 

From Maria: Given a six by six square, how rectangles are there in the square? Answered by Stephen La Rocque. 





A Farmer's pasture 
20071019 

From Jennifer: A Farmer's pasture measures 100 feet by 108 feet. Each cow needs 4 square yards of pasture to have enough grass.
How many Cows should the farmer put in this pasture?
If he builds a fence around the pasture 5 feet inside the edge, how much fencing would he need?
Does this change the number of cows that can be kept in the pasture?
If so, why ? Answered by Penny Nom. 





How many square inches are there in 97 acres? 
20071018 

From Glenda: How many square inches are there in 97 acres? Answered by Penny Nom. 





A triangular lot 
20071017 

From Brian: Seeking the square footage of a triangular property lot, dimensions are: 620 X 620X 720. Answered by Penny Nom and Melanie Tyrer. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





How many sq yards did i use? 
20071003 

From Rose: i used 12 x 19 of carpet. how many sq yards did i use? What is the formula for this? Answered by Victoria West. 





Cubic meters, square feet and office space 
20070925 

From Kathryn: Can someone please help and let me know how do you convert 11 cubic meters into square footage? Answered by Steve La Rocque and Harley Weston. 





The diagonal of a square 
20070923 

From Nasreen: A(7,2) and C(1,4) are two vertices of a square ABCD
find in the form ax+by=c the equation of the diagonal BD Answered by Stephen La Rocque. 





A 5 by 5 checkerboard 
20070917 

From Darren: Hi, I'm Darren and i have some questions to ask you about this problem:
In a 5 by 5 checkerboard : how many 2 by 2 squares are there,
what other sizes of squares do you need to count and how many of of each size of squares
can you find; how many squares did you find in all Answered by Victoria West. 





14/square root 3 
20070912 

From Prudence: How to solve this question?
1  4/√3 Answered by Penny Nom. 





Yards by yards to square metres 
20070910 

From Julie: I need a formula to translate linear yards so 36" by 54" to square meters.
So first I need to square the yard and translate it to square meters. Answered by Stephen La Rocque and Penny Nom. 





Does every number have a square root? 
20070910 

From Cheryl: Does every number have a square root? Answered by Harley Weston. 





Is there a way I can calculate correct square footage for odd shapes? 
20070831 

From Tom: I manage a golf course, and we are about to over seed the course for the upcoming winter months. We will be over seeding all greens, fairways, and tee boxes. Noone of the area that we will be placing seed on is a regular shape. The closest shapes they would be is a circle, rectangle or square, but most of them are all odd CURVED shapes. I know what the equation is for Square ft., and I know how many Square ft. are in an acre, but I need to be precise with the amount of seed I order. Is there a way I can calculate correct square footage for odd shapes. Answered by Harley Weston. 





Simplify (square root of)200 
20070828 

From melissa: how do you simplify:
(square root of)200 Answered by Penny Nom. 





32,648 square footage = how much land? 
20070822 

From Elizabeth: 1. What amount of Land = an acre?
2. 32,648 square footage = how much land? Answered by Penny Nom. 





A square problem 
20070819 

From Amanda: Consider a square with side s, diagonal d, area A and perimeter P.
a) express the diagonal in terms of the side.
b) express the area in terms of the diagonal. Answered by Stephen La Rocque. 





The area of a five sided lot 
20070819 

From Karyn: I have been looking at your site, but I am still confused as to how to
figure out the exact square footage of my irregular lot (since it is a gradual fan
lot from the front, and triangles out in the back). Answered by Harley Weston. 





Two squares 
20070818 

From Jerry: The vertex E of a square EFGH is inside a square ABCD. The vertices F, G and H are outside the square ABCD. The side EF meets the side CD at X and the side EH meets the side AD at Y. If EX = EY, prove that E lies on BD. Answered by Chris Fisher. 





An octagon from a square 
20070815 

From Dian: Okay, here is my problem. I have a 21" square and want to make it into an octagon. I am 61 and mathematically challenged. What I need to know is how many inches to each angle? I want this to be accurate as I am using it for a pattern. Answered by Penny Nom. 





How many square feet are in 1.24 acres? 
20070815 

From Karen: how many square feet are in 1.24 acres Answered by Penny Nom. 





The area and perimeter of a rectangle 
20070815 

From Brooklyn: Is there a way to find the perimeter of a rectangle if you have the area, or vice versa? If so, what is the equation? Answered by Leeanne Boehm and Penny Nom. 





How many square meters are there? 
20070813 

From jane: if a room is 4meters by 5meters,how many square meters are there? Answered by Penny Nom. 





Find all numbers which are both squares and cubes 
20070730 

From Arul: what is the easiest way to find the number which is both a square and a cube?
the numbers i know are 64 and 729 which is both a sqr and a cube.
i took long time to solve this.. is there any easier way? Answered by Steve La Rocque. 





Cubic metres of topsoil 
20070725 

From Laurie: How do I convert cubic meters to square meters? Answered by Harley Weston. 





Simplifying an algebraic fraction expression 
20070725 

From Jessica: How do I simplify b/(b^{2}25) + 5/(b+5)  6/b? Answered by Stephen La Rocque. 





The area of a property 
20070717 

From Mary: I currently have an opportunity to sell my property to a business and they would like me to send a proposal to them with details.
I need to know the square footage of my property and have tried using your formula from similar questions. The dimensions of my property are as follows
front line facing street: 19.908 m
right side : 37.338 m
back line : 29.779 m
left side : 43.983m
The front line and the right side are at right angles to each other. Can you formulate and reply? Thank you Mary Answered by Harley Weston. 





Divide a square into seven pieces 
20070717 

From suzette: how can you divide a square into 7 equal sizes and shapes? Answered by Penny Nom. 





A square and an equilateral triangle have the same perimeter. 
20070702 

From eve: I am trying to help my daughter with the following problem: A square and an equilateral triangle have the same perimeter. The sum of one side of the square and one side of the triangle equals 28 cm.
Find the sides of the figures. Answered by Penny Nom. 





Using Heron's Formula to help maximize the area of a triangle 
20070627 

From Claire: Given one side of a triangle is 4 cm and the ratio 1:3 for the other 2 sides. What is the largest area of the triangle? Answered by Stephen La Rocque and Harley Weston. 





The sum of angles in a square is three hundred and sixty degrees 
20070621 

From victor: can you please send to me a formalize proof for the assertion that, the sum of angles in a square is three hundred and sixty degrees. i will be grateful to hear from you Answered by Stephen La Rocque. 





Simplifying complex denominators 
20070621 

From Krys: How do I simplify completely?
((4+i ) / (3+i ))  ((2i ) / (5i )) Answered by Stephen La Rocque. 





Finding the center of an ellipse 
20070620 

From Sima: find the center of the ellipse with the equation 3x^2 +4y^2+18x32y5=0 Answered by Penny Nom. 





How many acres is 1.8 sq miles? 
20070619 

From Jordanne: How many acres is 1.8sq miles? Answered by Penny Nom. 





A square and a rectangle 
20070619 

From Clarence: What is the difference between rectangle and a square Answered by Penny Nom. 





A circle inside a square 
20070531 

From Mer: there is a circle inside a square... there is a shaded rectangle that measures 5mm X 10mm and they want to know what the radius is. The edge of the shaded rectangle touches a point on the circle. Answered by Penny Nom. 





Cubic inches and square feet 
20070531 

From keith: is it possible to convert cubic inches to square feet.thanx Answered by Stephen La Rocque. 





A bag of concrete 
20070529 

From rick: I have a bag of concrete that will cover .525 cubic feet of space.
How many square feet will the same bag cover? Answered by Penny Nom. 





Is a square also a right trapezoid? 
20070524 

From Don: Is a square also a right trapezoid? Answered by Stephen La Rocque. 





Simplifying a square root 
20070524 

From Leigh: I am trying to help my son. Simplify sq root 81 x to the 2nd power y to the 12th power. Answered by Stephen La Rocque. 





Finding square roots 
20070517 

From Chandler: I would like an easy way to find the square root of a number. Answered by Gabriel Potter. 





Counting squares 
20070512 

From Bridget: Explain how many squares there are on a board measuring 4 by 4 units, Answered by Stephen La Rocque and Penny Nom. 





Area of a pentagonal lot 
20070509 

From Mimi: I would like to know the square footage of a pentagon with the
following measurements:
Property is .43 of an Acre
Front: 57.11'
NW: 105.78'
S: 120'
SE: 145'
E: 102.86'
I don't want you to try to show me how to work thru the problem since
I will never comprehend it. For some reason, I am unable to perform these
kinds of equations. I will greatly appreciate your help. Answered by Penny Nom. 





A problem involving squarefree integers 
20070507 

From Andrew: I was told that if x > y (integers); then x would never exactly =
divide y^n (n integer > 1) if (x,y) =3D 1 ; or if x is "square =
free". Is the latter true and why? Answered by Stephen La Rocque and Penny Nom. 





What is the square root of 729 to the third power? 
20070425 

From Tori: What is the square root of 729 to the third power? Answered by Penny Nom. 





Using the "difference of squares" formula how do I compute 27 * 33? 
20070402 

From Sarah: Using the "difference of squares" formula how do I compute 27 * 33? Answered by Penny Nom. 





5 square metres 
20070328 

From Allan: please confirm if an area of 5 square metres is different from 5m^2 (5metres squared) Answered by Penny Nom. 





Inscribed square in inscribed circle 
20070325 

From Confuzzled: "The largest possible circle is drawn inside a square. Then the largest possible square is drawn inside this circle. What is the area of the inner square as a fraction of the area of the outer square?"
This is a question from the Grade 8 Gauss contest and I don't know how to work it out without drawing it. My teacher says it's possible but I still don't get it. Please help!!! Answered by Stephen La Rocque. 





What will our square footage size be after appropriation? 
20070317 

From Melissa: I have a rectangular lot of 110.0 feet by 396.0 feet. When we sell the District will take 2.38 meters off the front for appropriation. I believe we currently have a 1 acre lot? What will our sqaure footage size be after appropriation?
Thanks,
Melissa Answered by Penny Nom. 





The square of an odd number 
20070316 

From Samantha: Is the square of an odd number always odd? Answered by Stephen La Rocque and Penny Nom. 





Square metres, cubic metres and timber 
20070315 

From remy: our timber is in square meter , our supplier is using cubic meter,
how do I convert from cubic meter to square meter.
Many thanks
remy Answered by Harley Weston. 





A square 
20070302 

From Jake: how many sides does a square have? Answered by Sara Ulmer. 





Factoring polynomials 
20070214 

From Joe: I am in the eighth grade, and we are learning the equivalent of Algebra 2. I have no ides how to factor (x2)(x^21)6x6 You help is most aprreciated. Thank you! Joe Answered by Stephen La Rocque. 





Cost per square foot 
20070214 

From llinden: how do you figure out the cost of square footage? the amount per sq ft is $28 Thank you Answered by Gabriel Potter. 





Square centimeters 
20070212 

From Ivan: how many square centimeters are in a rectangle that is 210 centimeters long by 39 centimeters wide.? thank you Answered by Karen McIver and Melanie Tyrer. 





Rectangles and squares 
20070131 

From Shelby: I am doing homework and I need to know why squares are rectangles but not all rectangles are squares? Answered by Penny Nom. 





Square meters and cubic meters 
20070130 

From Fiel: How do i convert square meter to cubic meter? Answered by Penny Nom. 





converting square miles into square meters 
20070127 

From Susan: how do you convert square miles into square meters Answered by Stephen La Rocque. 





Can you make a square out of a right triangle by using only one straight line? 
20070126 

From Debra: Can you make a square out of a right triangle by using only one straight line? Answered by Stephen La Rocque and Penny Nom. 





A lumber yard receives 24 studs in a bundle 
20070123 

From Roxanne: A lumber yard receives 24 studs in a bundle that contains 25 row (or layers) of studs with 20 studs in each row. A 2X4 stus ia actually 1 1/2'' X 3 1/2'' X 92 5/8 Find the cross sectional area of a bindle in square inches Find the volume of the bundle in cubic feet Answered by Stephen La Rocque. 





The square footage of a lot 
20070122 

From A parent: I HAVE A LOT THAT IS 50FT. BY 95.5 FEET HOW MANY SQ.FEET. Answered by Penny Nom. 





A statistics question 
20070107 

From Rick: For many years TV executives used the guideline that 30 percent of the audience were watching each of the primetime networks and 10 percent were watching cable stations on a weekday night. A random sample of 500 viewers in the TampaSt Petersburg, Florida, area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station. At the 0.05 significance level, can we conclude that the guideline is still reasonable? Answered by Penny Nom. 





5sqrt2+3 
20070107 

From Mike: I don't understand why 5sqrt2+3 is the correct answer over 5sqrt 5 Answered by Penny Nom. 





An octagon inscribed in a square 
20061229 

From Richard: An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. The perimeter of the square is 108 centimeters. What is the number of square centimeters in the area of the octagon? Answered by Walter Whiteley. 





Prove that square root of 3 is irrational. 
20061221 

From Humera: Prove that square root of 3 is irrational. Answered by Stephen La Rocque. 





Miles, square feet and acres 
20061218 

From Emily: How do you convert miles to square feet? I have to convert 2.86 miles to square feet and then convert 72.5 acres to square feet and add them together. I looked on your website and what does the word hence mean? Answered by Penny Nom. 





How many squares are there on a checkerboard 
20061217 

From Tania: how many squares are there altogether on the checkerboard (including the 64 small squares)? Answered by Penny Nom. 





Factoring m^49^n 
20061207 

From Josh: I can not figure out how to completely factor m^49^n. Answered by Penny Nom. 





The square footage of an irregular lot 
20061207 

From Lori: If I have a rectangular irregular sized lot with the following:
A  110.53' B  159.87' C  127.28' D  165.86'
How do I determine the square footage? Answered by Penny Nom. 





1X2X3X4+1=5^5 
20061123 

From Liza: 1X2X3X4+1=5 square 2x3x4x5+1=11 square What is the rule for this? Answered by Stephen La Rocque and Penny Nom. 





The square footage of 1.29 acres 
20061120 

From Steve: What is the approx. square footage of 1.29 acres? Answered by Penny Nom. 





The rate of change of the perimeter of a square 
20061107 

From Karli: Find the rate of change of the perimeter of a square with respect to its area. Answered by Stephen La Rocque. 





What's 3x squared? 
20061102 

From Cath: What's 3x squared? Answered by Penny Nom. 





I have a 3000 sq ft house ... 
20061010 

From Ann: I have a 3000 sq ft house and need to use flea foggers. Each fogger treats 6000 cubic feet. How many do I need? Answered by Stephen La Rocque. 





Squaring numbers 
20061008 

From Timothy: did anyone ever try to teach that the easiest way to find the next square in a group of numbers is to add the next odd number in the sequence. for example: 1 squared is 1, 2 squared is 4,difference of 3.the next odd number is 5 so the next square would be 4 +5 or 9 Answered by Paul Betts and Penny Nom. 





A 5x2 rectangle 
20061003 

From Stanley: Cut a 5x2 rectangle into 4 pieces, and then put them back into as a square. Answered by Claude Tardif and Penny Nom. 





Two word problems 
20061002 

From Eve:
1. A surveyor's map shows a plan for the rectangular rose garden whose area is
a^{2}+25ab350b^{2}. Find an algebraic expression for the length and width. If a=20 ft and b=10 feet, find the actual dimensions of the garden.
2.A square is enclosed in a circle. The area of the square is (4r^{2}32r+64)sq cm and the area of the circle is 484r^{2} sq cm. Write a polynomial in factored form to represent the difference of the two areas.
Answered by Stephen La Rocque. 





How do you convert square inches to square yards 
20060928 

From A student: how do you convert square inches to square yards Answered by Stephen La Rocque and Penny Nom. 





Help me prove that the square root of 6 is irrational 
20060923 

From Sylvia: Could you please help me prove that the square root of 6 is irrational ? Answered by Stephen La Rocque. 





Sqyare yards and cubic yards 
20060921 

From Kevin: I WOULD LIKE TO KNOW HOW TO CONVERT SQUARE YARDS INTO CUBIC YARDS OF MATERAIL (DIRT) Answered by Penny Nom. 





The square footage of my property 
20060917 

From Jack: I have been trying to calculate the square footage of my property, without success. The measurements are below.
Is there a simple formula that can be used based upon the outside parameters? Or, is there a simple way to calculate the square footage? Answered by Stephen La Rocque and Penny Nom. 





A square palindrome 
20060911 

From Liz: What is the least threedigit palindrome that is a square number? Answered by Stephen La Rocque. 





What is the length of one side of 10 sq acre 
20060830 

From Rick: what is the length of one side of 10 sq acre Answered by Penny Nom. 





Converting sq ft to sq meters 
20060803 

From JB: I would like to convert 2700 square feet into square meters. Answered by Penny Nom. 





The lot is a very odd shape 
20060720 

From Liz: I have a square footage question. I'm looking at buying a piece of land and would like to know how to calculate the square footage of it. The lot is a very odd shape and I have attached a drawing of the lot: Answered by Stephen La Rocque. 





Finding square footage from lengths in inches 
20060714 

From Ann: How do I find out the square footage of a window 45" by 22" and 43" by 35.5"? Answered by Stephen La Rocque. 





Convert 13ft by 10ft room area into square feet 
20060618 

From Marlene: want to convert 13ft by 10ft room area into square feet Answered by Penny Nom. 





Square feet and linear feet 
20060610 

From Richard: Need to know how many linear ft are in 2800 sq.ft Answered by Penny Nom. 





Buying some carpet 
20060605 

From Russ: My room is 24 ft. long and 17 ft. wide. I need to know how many square feet are in 1 yd.² Answered by Penny Nom. 





Square feet and acres 
20060519 

From Lisa: 1.12 acre= ???? sq ft
1.043 acre= ???? sq ft
I work in the loan department and I do appraisal reviews but I use square feet to determine my values. Answered by Penny Nom. 





The square root of 4 
20060507 

From MaryBeth: I am a high school teacher of Algebra. I was recently teaching square roots to my students and an interesting question arose. Our textbook seems to be inconsistent. I was hoping you might be able to give our department your opinion on who is correct as we are divided on the correct way to teach this. When you take the square root of a number, you get two answers, a positive root and a negative root, correct? Our book presents this as √4 = 2 and √4 = 2 and ±√4 = ±2. Shouldn't it be taught as there are always two roots, the positive and the negative? It seems to me, there is really no reason to have to use the ± as there are always 2 roots, the positive and the negative. But if the negative sign is given then only the negative answer should be given? What's your take?
Answered by Penny Nom. 





A hallway in an old house 
20060506 

From Sabrina: I am trying to determine how many square feet is in a room that is not square or rectangular. It has basically 5 walls of different lengths, it is acutely considered a hallway in an old house, how can I figure out the footage, the Length times Width requires to much wasted materials Answered by Penny Nom. 





5 square miles or a 5mile square? 
20060503 

From Rosemary: I am an interpreter in our Historical Museum. From what I received, I have always told my guests that when the Connecticut Land Company sold the Western Reserve land, 5 square miles constituted a township. I was corrected yesterday by someone who said it should have been a 5mile square. What is the difference? Hope you can help. Answered by Penny Nom. 





If the perimeter of a square is 1 foot, what is its area? 
20060427 

From Larry: If the perimeter of a square is 1 foot, its area is how many square inches? Answered by Stephen La Rocque. 





Which has more pizza? 
20060419 

From Kristine: Which has more area: a round pizza that is 16 inches in diameter or three square pieces of pizza that are 8.5 inches on each side? Answered by Stephen La Rocque. 





Perimeter of a triangle atop a square 
20060413 

From Mary: There is an (irregular) pentagon that is made up of a square and a triangle. The triangle is directly on top of the square. The triangle is a right triangle. One of the angles is 45 degrees. One of the sides of the triangle is 4. What is the perimeter of the pentagon? Answered by Penny Nom. 





Finding square roots 
20060412 

From Fehmida: I would like to know about tricks or formulas to do complicated square roots.
ex. square root of 1029 Answered by Penny Nom and Steve La Rocque. 





A square in a circle 
20060405 

From Lisa: A square is inscribed in a circle. Determine the percent of the circle's area that is outside the square. Answered by Stephen La Rocque. 





Acres 
20060325 

From Judy: How do you turn land measurements into acres
Such as piece of property is 45 x 167 Answered by Penny Nom. 





Two squares 
20060325 

From Debbie: A small square is constructed. Then a new square is made by increasing each side by 2 meters. The perimeter of the new square is 3 meters shorter than 5 times the length of one side of the original square. Find the dimension of the original square Answered by Stephen La Rocque. 





The square footage of an area in my backyard 
20060317 

From Kim: I need to find out how to calculate the square footage of an area in my backyard that is in the shape of a "slice of pie". There are two sides that are straight lines that come together at the top to form a point, and then at the bottom is a curved line that joins the two other lines together. I need to figure out how to calculate the square footage that is inside the area. Answered by Penny Nom. 





Adding a cellar 
20060314 

From Spencer:
You want to add a cellar to your store. The construction company told you it would cost $5.90 per cubic yard to dig the cellar plus $20.00 per square ft. to finish it.
How much will it cost to add a cellar 36 feet long, 14 feet wide, and 8 feet deep?
Answered by Stephen La Rocque. 





Square roots 
20060307 

From Diana: Find each square root Answered by Harley Weston. 





the size of a lot is 300 sqm, what is the square feet conversion? 
20060211 

From JC: the size of a lot is 300 sqm, what is the square feet conversion? Answered by Penny Nom. 





How do I calculate feet and inches to sq ft? 
20060109 

From Rebecca: How do I calculate feet and inches to sq ft? Answered by Penny Nom. 





40 acres= how many square meters? 
20060107 

From Janelle: 40 acres= how many meters? Answered by Penny Nom. 





2800 sq meters 
20051227 

From Roger: I am going to buy some land and its 2800 sq meters. Is it a acre? Answered by Penny. 





Find the nth term 
20051214 

From Kevin: How do i find the nth term of 1 4 9 16 25 36 Answered by Penny Nom. 





The perimeter of a collection of squares 
20051211 

From Catherine: using 12 squares, make a number of patterns (squares joined). Find the perimeters. Find out how many points in the shape have four radiating lines i.e. are two lines intersecting. Write an equation to state the relationship between the lines and the perimeter. Answered by Penny Nom. 





A one acre square 
20051201 

From David: I know there are 43,560 square feet in 1 acre of land.
If that acre were completely square what would be the perimeter of the square.
I am trying to construct a 1 acre pen for livestock.
Answered by penny Nom. 





Tables with perfect squares 
20051130 

From Craig: A table consists of eleven columns. Reading across the first row of the table we find the numbers 1991, 1992, 1993,..., 2000, 2001. In the other rows, each entry in the table is 13 greater than the entry above it, and the table continues indefinitely. If a vertical column is chosen at random, then the probability of that column containing a perfect square is: Answered by Claude Tardif. 





The square root of i 
20051130 

From Kevin:
If the square root of 1 is i, what is the square root of i?
How can you find the log of a negative number?
What is the log of 1?
Answered by Claude Tardif. 





A block pyramid 
20051105 

From Kyle: if i make a block pyramid and it puts a new perimeter around it every time, for example the first layer will be 1 block across (area=1), the second layer will be 3 blocks across (area=9), the third layer will be 5 blocks across (area=15),etc. The normal block pyramid. I have figured out that in order to figure out the number of blocks needed for a certain level, the equation is (2x1)2 or (2x1)(2x1), where x is equal to the level. For example, on the fourth level, the equation tells you that it will have an area of 49. How would i make an equation for the total number of blocks up to the level. For example, in order to complete 1 level you need 1 block, for 2 levels you need 10 blocks, for three levels you need 35 blocks, and for 4 levels you need 84 blocks. Answered by Penny Nom. 





7000 sq feet = ? acres ??? 
20051105 

From Victor: 7000 sq feet = ? acres ??? Answered by Penny Nom. 





An odd number of factors 
20051006 

From Ramneek: What is the common name used for numbers that have an odd number of factors? Answered by Claude Tardif. 





One square mile 
20050911 

From Rudy: I know that there are 27,878,400 sq ft in a square mile and that there are 640 acres in a sq mile. But how do I figure out the measurement of each acre. If I could make every acre a square what would it's measurement be? Answered by Penny Nom. 





A typical farm 
20050901 

From Pagedi: A typical farm is about 700 acres. How many square miles is this? Please show me the work so, that I will know I to perform this problem myself. Answered by Penny Nom. 





1,4,9,1,6,2,5,3,6,4,9,6,4,8,1 
20050830 

From Liz: Find the next four numbers to the sequence 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,___,___,___,___. Answered by Penny Nom. 





The length of a lot 
20050828 

From Billy: If I have 3 acres and the front is 300 ft across how many feet would I go down the sides to equal 3 acres? Answered by Penny Nom. 





A perfect square that is equal to 1 acre 
20050731 

From Shannon: If you have a perfect square that is equal to 1 acre, what is the length of the sides and how do you do it? Answered by Penny Nom. 





How many tiles do I need? 
20050720 

From Jeannette: I am putting up backsplash tile in my kitchen and I need to know how many tiles I would need to use for about 45 square feet using 4x4 tiles. Answered by Penny Nom. 





The size of a lot 
20050609 

From Bob: Is it possible to determine the square footage and acreage of a residential lot that's straight on 3 sides, and triangular on the 4th side?
As shown in the crude sketch below, the two legs of the triangle at the back end of the lot are 61' and 62'. Answered by Penny. 





Square feet and cubic feet 
20050530 

From Kim: Is there a relationship between square feet and cubic feet? Answered by Penny Nom. 





A triangular lot 
20050521 

From Linda: I am looking to purchase a piece of property, and I need some help trying
to figure out the square footage of the land. I know that
normally if I multiply the length and width I could get my answer. However,
this piece of land is an odd shape and has 3 measurements. Can you
please help me.
The measurements for this piece of land is:
97.8'
201.2'
139.7' Answered by Penny Nom. 





Explain why 3(x+2) = 3x+2 is incorrect 
20050328 

From Cynthia: An algebra student incorrectly used the distributive property and wrote 3(x+2) = 3x+2. How would you explain to him the correct result, without the use of the distributive law?
Explain why the square of the sum of two numbers is different from the sum of the squares of two numbers. Answered by Penny Nom. 





The square root of 2 
20050312 

From Madhumita: From Pythagoras theorem we can draw square root 2 as a finite distance but it is irrational number which is endless. Explain how we can equate these two. Answered by Harley Weston. 





What is the least threedigit palindrome that is a square number? 
20050212 

From Ben: What is the least threedigit palindrome that is a square number? Answered by Chris Fisher and Penny Nom. 





Is a square a rectangle? 
20041121 

From Carol: I am a teacher. In an FCAT sixth grade review test, there was a question to the students to draw a square and then they referred to it as a rectangle.
What is the definition that makes a rectangle a square that can be taught to the students without confusing them. Answered by Walter Whiteley. 





Largest square inside a circle 
20041025 

From Bob: my granddaughter asked
what is the largest size square in inches
would fit in a 60 inch circle?
I believe it to be around 42.3 inches but
would like to teach her how to do it mathematically. Answered by Penny Nom. 





Square roots and inequalities 
20041025 

From Waheed: Q1. What is the simplest way of finding a square root of any number using just a pen and paper? (I am asking this question because I browsed a few sites a didn't find any method that is simpler than the one I use. so I am just curious.)
Q2. Is it possible that you take an equation and turn it into an inequality by performing same mathematical operations on both sides? Answered by Claude Tardif and Penny Nom. 





A square footage problem 
20041019 

From Jerome: I have a peice of property that is almost a triangle but not exactly about 280 frontage with the side lines at 228 and 237
I was told I had about one acre plus a little, a developer says I have 33,000 sq ft. and I would like to know what the real result is Answered by Penny Nom. 





A binomial squared 
20040919 

From John: Can you explain the steps
for me, that get you from (a  b)^{2} to a^{2} 
2ab + b^{2} Answered by Penny Nom. 





The distance formula 
20040904 

From Joe: Why do we use square roots and squares in the distance formula Wholdnt they cancel each other out? Answered by Claude Tardif. 





The area of a lot 
20040822 

From Cassie: I'm in the process of purchasing some land and I'm trying to figure out the square footage of the property. Unfortunately, it's be a while since I had to remember this type of formula. The property is 140 ft on left side, across the back it is 220.61 ft, the right side is 167.52 ft, the frontage is 105 ft. Answered by Penny Nom. 





2.79 acres 
20040811 

From Helen: What would the square footage be of 2.79 acres? Answered by Penny Nom. 





Factoring 
20040719 

From A student: Factor completely:
3x3  24y3
54x6 + 16y3
16xy  4x  4y  1
0.09x2  0.16y2 Answered by Penny Nom. 





Area of a lot 
20040617 

From Mike: Could you please figure out the square footage and acreage of my lot? One side is 228 feet, another is 150 feet, another is 80 feet, and the last side is 164 feet. My house is in the middle and it is 62 feet by 37 feet. Is that subtracted from the total? I would like to know this when I have to buy fertilizer.
Answered by Penny Nom. 





ChiSquared 
20040505 

From Gillian: OF75 PEOPLE, 43 ARE EXPOSED TO A VIRUS AND BECOME ILL. 11 PEOPLE ARE EXPOSED AND DO NOT BECOME ILL. 3 PEOPLE ARE NOT EXPOSED AND BECOME ILL. 18 PEOPLE ARE NOT EXPOSED AND DO NOT BECOME ILL. THE ATTACK RATE IS 80% FOR THOSE EXPOSED AND 14% FOR THOSE NOT EXPOSED. THE RELATIVE RISK IS 5.7. CAN YOU EXPLAIN TO ME HOW TO CALCULATE A CHI SQUARE TEST FROM THIS. Answered by Penny Nom. 





3x squared  27 / x + 3 
20040504 

From Stef: 3x squared  27 / x + 3 Answered by Penny Nom. 





square root 125 x 16 
20040423 

From Mike: how do you simplify a square root of " square root 125 x16" when x is a variable... i don't really get how to do this.... Answered by Penny Nom. 





Some factoring problems 
20040415 

From KJ: Factor these:
x^{3}+125 > (x+5)^{3}
8x^{3}27 > (?)
x^{2}+36 > (x+6)^{2}
x^{4}5x^{2}+4 > (?) Answered by Penny Nom. 





A geometry problem 
20040304 

From Jennifer: I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o Answered by Chris Fisher. 





Acres and square miles 
20040217 

From Richard:
How many acres are in .17 square miles? and How many acres are in .6 square miles?
The two areas I am requesting information about are Vatican City and San Marino, the two smallest countries in the world. If I can transfer the sq. miles into acres , I can relate the size of these countries to our school grounds and the students will better understand their sizes.
Answered by Penny Nom. 





Twelve acres 
20040113 

From Heather: I am looking at buying a property that includes 12 Acres of land and I am trying to visualize what this size is equivalent to. I have searched your site and figured out how many square feet it is but I was hoping that you could apply 12 Acres to something tangible, like a football field! Answered by Penny Nom. 





The square footage of an acre 
20040112 

From Paul: What is the square footage of an acre of land assuming all four sides are
equal in length. Answered by Penny Nom. 





400, 100 and 2500 
20031221 

From A student: A person likes 400 but dislikes 300
He also likes l00 but dislikes 99
He also likes 2500 but
dislikes 2400
Which of the following does John like
900, 1000, 1100 or 2400
Answered by Penny Nom. 





Difference of squares 
20031124 

From Susie:
Factor assuming that n is a positive #
Problem: (I will give it to you in words beacuse I don't know how to do exponents on the computer.)
Fortyfive r to the 2n power minus five s to the 4n power.
I was hoping you could walk me through it not just give me the answer.
Answered by Penny Nom. 





root24 = 2 root6 
20031113 

From Burke: I know that all algerbra can be represented visually, for example: Y=9x+3 is a line on a two dimentional plane. Could Math Central please send me a visual representation of the proccess of simplifying square root like root24 equals 2root6 Answered by Penny Nom. 





A least squares line 
20031109 

From Michelle: Hooke's Law asserts that the magnitude of the force required to hold a spring is a linear function of the extension e of the spring. That is, f = e0 + ke where k and e0 are constants depending only on the spring. The following data was collected for a spring; e: 9 , 11 , 12 , 16 , 19 f : 33 , 38 , 43 , 54 , 61 FIND the least square line f= B0 + B1x approximating this data and use it to approximate k. Answered by Penny Nom. 





Squares in a rectangle 
20031021 

From Raj:
Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle. If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares. Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle. Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle? Answered by Chris Fisher. 





Making a square 
20030907 

From A student: if I am given any number (say 80 for example), how may I determine the smallest whole number integer which when multipled by it will yield a square number ? In other words if I express this as: 80Ý*ÝnÝ=ÝsquareÝnumber, what is the least value of n which will yield a square. Answered by Penny Nom. 





Acres 
20030813 

From A landowner: Can you please tell me how many total acres the following measurements would equal? 280 feet by 80 feet 220 feet by 70 feet 200 feet by 75 feet Answered by Penny Nom. 





Numbers John likes 
20030620 

From Steve: John likes 400 but not 300; he likes 100 but not 99; he likes 2500 but not 2400.
Which does he like? 900 1000 1100 1200 Answered by Penny Nom. 





2/sqrt(2) 
20030507 

From Mike: I was looking at an example of csc 45 deg where csc = hyp / opp = 1 / (sqrt(2) / 2) = 2 / sqrt(2) = sqrt(2) I just don't get this. If sqrt(2) = 1.4142145..... How can 2 / sqrt(2) = sqrt(2) as the example shows? Answered by Penny Nom. 





The square of my age was the same as the year 
20030414 

From Pat: Augustus de Morgan wrote in 1864, "At some point in my life, the square of my age was the same as the year." When was he born? Answered by Penny Nom. 





Can twice a square be a square? 
20030325 

From Mike: The other day it occurred to some students that they could think of no square number which is an integer, which can be divided into two equal square numbers which are intergers, Or put another way, no squared integer when doubled can equal another square integer. For example 5 squared plus 5 squared is 50, but 50 is not a square number. Answered by Walter Whiteley and Claude Tardif. 





Can a square be a rhombus? 
20030304 

From Beth: Can a square be a rhombus? Some sources say yes, some say no. Some sources define a rhombus as a quadrilateral and parallelogram with equal sides, but without right angles. Some sources say a square is a special case of a rhombus. Clarity, please! Answered by Walter Whiteley. 





Can a square be considered a rectangle? 
20030227 

From Carla:
Can a square be considered a rectangle? (since opposite sides are same length and parallel) Would a regular hexagon or octagon be considered a parallelogram since its opposite sides are parallel? or does a parallelogram HAVE to have only 4 sides? Answered by Penny Nom. 





A section of land 
20030225 

From Bev: How many acres in a section of land? How many square miles is in a secion of land? Answered by Penny Nom. 





0.027 acres 
20030116 

From Cory Lee: How many square feet are in How many square feet are in .027 acres?? Answered by Penny Nom. 





Factoring 
20021211 

From Larry: Question:
how do u factor trinonmials
EX: X^{ 3} + Y^{ 3}
X^{ 3}  8Y^{ 3}
8X^{ 2}  72
64A^{ 3}  125B^{ 6} Answered by Penny Nom. 





Is a square a rectangle? 
20021020 

From Nona: Are squares rectangles? Third grade math teacher told a student this was true. Grandmother needs confirmation on this! Answered by Claude Tardif and Harley Weston. 





8 squares from 12 sticks 
20021008 

From A student: If you have 12 sticks the same size, how do you make them into 8 squares? Answered by Claude Tardif. 





A square of tiles 
20020830 

From Rosa: How do I go about finding a formula for the number of tiles I would need to add to an arbitrary square to get to the next sized square? Answered by Penny Nom. 





When is 1! + 2! + 3! + ... + x! a square? 
20020819 

From Sarathy: Solve : 1! + 2! + 3! + ... + x! = y^{ 2} How do i find the solutions ? Answered by Claude tardif. 





0.63 of an acre 
20020608 

From Sherry: how many square feet are in 0.63 of an acre Answered by Penny Nom. 





Constructing the square root of 3 
20020607 

From Allan: I am a Math 7/8 teacher. I was wondering how you would show a student how to find the exact location of the square root of three on the number line using just a compass and a straight edge. Answered by Penny Nom. 





Square numbers 
20020501 

From Sally: Is one considered a square number? Answered by Penny Nom. 





The square root of four 
20020413 

From Frank: In a recent quiz we where asked the square root of four. The quizmaster gave the answer as not only 2 but also 2. Being pedantic I queried this. Although 2 squared is 4, does it follow that the root of 4 is 2 Can you enlighten us? Answered by Claude Tardif and Penny Nom. 





Sodding the yard 
20020408 

From Craig: my parents want to lay sod in our back yard. the sod cost $2.00 per square foot. The size of our yard is 20x20 and 26x41 Answered by Penny Nom. 





Area of an octagon 
20020401 

From Someone: What is the actual square footage of a 12' octagon? Answered by Penny Nom. 





The square root of i 
20020314 

From Arlene: what is the square root of i, if i=x+yi? what is the square root of 1i? i'm getting problems like these in which I do not understand. Answered by Harley Weston. 





The square root of 2 
20020305 

From Roger: Does two (2) have a square root or do the numbers just keep going? Are there any other numbers that behave like two when it comes to extracting the square root? Answered by Penny Nom. 





Double square roots 
20020217 

From Ali: i have a question about how to do double square roots with variables and powers. example : v/"" v/"" 81y^{8} Answered by Harley Weston. 





Number conversions and averages 
20020203 

From A student: A table has the measurements of 1.6m by 2m, how much material is needed to cover table? I converted to cm then multiplied but got an answer of 32000cm ,so I divide by 100 to get to metres  the answer was 320 which I know is wrong  please explain!! Also I need to explain in my own words what an 'average' is and I am struggling. Answered by Penny Nom. 





Square arrangements of clovers 
20020203 

From Cassie: Clyde had a strange fascination with numbers. One day he decided to mount his 4 leaf clover collection in groups of square numbers.he took a long piece of butcher paper and glue and began this arduous task.There was 1 clover,4 clovers.and then 9 clovers in the third set. what would be in the seventh set of 4 leaf clovers? Answered by Penny Nom. 





A sequence 
20020116 

From Chris: I have spent two days trying to determine the pattern to the following set of numbers: 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,____. I need the next four numbers to the sequence. Answered by Claude Tardif. 





Linear regression 
20020116 

From Murray: If you have a set of coordinates (x[1],y[1]),(x[2],y[2]),...,(x[n],y[n]),find the value of m and b for which SIGMA[from 1 to m=n]AbsoluteValue(y[m]m*x[m]b) is at its absolute minimum. Answered by Harley Weston. 





Solving x^23x+5=0 
20011130 

From Katy: How do you find the solution to x^{2}3x+5=0? Answered by Penny Nom. 





Magic squares 
20011117 

From A student: 7th grader wanting to find solution to magic square:
place the integers from 5 to +10 in the magic square so that the total of each row, column, and diagonal is 10. The magic square is 4 squares x 4 squares. Answered by Penny Nom. 





(a+b) squared and a squared plus b squared 
20011114 

From Kristen:
(a+b)^{2} = a^{2} + b^{2} Is this true for all whole numbers, and why? Answered by Penny Nom. 





2=the square root of (2 + the square root of (2 + the square root of (2 +...))) 
20011105 

From Cynthia: justify algebreically, that: 2=the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + and so on, ....... Answered by Penny Nom. 





Squares of negative numbers 
20011103 

From Susana: I wanted to know if I can square a negative number..? Answered by Leeanne Boehm. 





Squaring the circle 
20011023 

From Margaret: I have the following question that I cannot answer on my own (I don't know where to begin): Is it possible construct a square whose area will equal the area of a given circle? Please Explain why or why not. Answered by Penny Nom. 





Some algebra 
20011015 

From James: I cannot figure these out I was wondering if you could help me? I have no one to answer my questions.  (7x^{2} – 3yz)^{2} – (7x^{2} + 3yz)^{2}
 Use Pascal’s triangle to expand (2x – y)^{4}
 8x^{3} y  x^{3} y^{4}
 (m + 3n)^{2} – 144
 12x^{4} y – 16x^{3} y^{2} – 60x^{2} y^{3}
 p^{3} q^{2} – 9p^{3} + 27q^{2} – 243
Answered by Peny Nom. 





Squares of one digit numbers 
20011015 

From Needa: What two twodigit numbers are each equal to their rightmost digit squared? Answered by Penny Nom. 





Area of a quilt 
20011014 

From Jack:
 how would you find the area of the quilt? which is a square
 how would you fined the area of each square?
Answered by Penny Nom. 





Acres 
20011010 

From Allison: how many feet are there in an acre? Answered by Chris Fisher. 





Pythagoras & magic squares 
20011009 

From John: My grandson became intrigued when he recently 'did' Pythagoras at elementary school. He was particularly interested in the 345 triangle, and the fact that his teacher told him there was also a 51213 triangle, i.e. both rightangled triangles with whole numbers for all three sides. He noticed that the shortest sides in the two triangles were consecutive odd numbers, 3 & 5, and he asked me if other right angled triangles existed, perhaps 'built' on 7, 9, 11 and so on. I didn't know where to start on this, but, after trying all sorts of ideas, we discovered that the centre number in a 3order 'magic square' was 5, i.e. (1+9)/2, and that 4 was 'one less'. Since the centre number in a 5order 'magic square' was 13 and that 12 was 'one less' he reckoned that he should test whether a 7order square would also generate a rightangled triangle for him. He found that 72425, arrived at by the above process, also worked! He tried a few more at random, and they all worked. He then asked me two questions I can't begin to answer ...  Is there a rightangled triangle whose sides are whole numbers for every triangle whose shortest side is a whole odd number? and
 Is each triangle unique (or, as he put it, can you only have one wholenumbersided rightangled triangle for each triangle whose shortest side is an odd number)?
Answered by Chris Fisher. 





The square root of 20 
20010918 

From Dianna: How do you simplify a square root? My daughter tells me that the square root of 20 simplified is 5root4 Answered by Penny Nom. 





The square root of 21/168 
20010910 

From A student: can you show me how to do this square root of 21/168 Answered by Penny Nom. 





Primes and square roots 
20010614 

From Paul: I have a bit of a math problem. It has to do with determining if a very large number is a prime. One method entails dividing the number by every smaller prime number. If any divide into it, it's not a prime. This would be a big job if the number was something like 400 digits long. Another way I read about was to take the square root of the number and test all the primes less than its square root. The explanation went like this: "When a number is divided by another number that is greater than its square root, the result is a number smaller than the square root. For example, the square root of 36 is 6. Dividing 36 by 2, a smaller number than 6, gives 18, a number that is larger than the square root. To prove that 37 is prime it is only necessary to divide it by primes less than 6, since if it had a prime factor greater than 6, it would have to have one less than 6 as well." I understand the explanation, up to the last sentence. I fail to see the underlying logic. Why if a prime factor exists below the square does one have to exist above the square too? The number 40 can be divided by the prime 2, a number below its square root, but no other primes can do this above its square root. Have I missed something? What's the logic here? Answered by Claude Tardif and Penny Nom. 





Teaching square roots 
20010508 

From Katie: My friend and I are doing a project. We have to teach our class about square roots. What is the easiest way to teach square roots to a class? Answered by Penny Nom. 





How many acres are in a square mile? 
20010504 

From Terri: How many acres are in a square mile? Answered by Judi McDonald. 





Are you overweight? 
20010503 

From Oneita: How do I square a number.....? My problem is : square your height in inches and take 4.25 percent of the result to determine if you are overweight. Answered by Claude Tardif. 





Squares of Fibonacci numbers 
20010424 

From Vandan: What discoveries can be made about the sum of squares of Fibonacci's Sequence? Answered by Penny Nom. 





Squares on a chess board 
20010411 

From Tom: It was once claimed that there are 204 squares on an ordinary chessboard (8sq. x 8sq.) Can you justify this claim? "PLEASE" include pictures. How many rectangles are there on an ordinary chessboard? (8sq. x 8sq.) "PLEASE" include pictures. Answered by Penny Nom. 





Dots on squared paper 
20010330 

From Tom: Consider some squared paper with lines 1cm. apart and dots where the lines cross. Place squares whose sides are whole numbers of centimetres on the paper in such a way that the sides of the squares always lie along the lines on the paper. For each square, find (a)the number of points inside the squares; (b)the number of points on the square and (c)the area of the square. How are these quantities related? Answered by Leeanne Boehm and Penny Nom. 





Radicals 
20010318 

From Nikki: 3) squareroot of x^{2} + 10x + 25 4) sixthroot of (m + 4)^{6} 5) cuberoot of 64r^{6}w^{15} . . . . Answered by Penny Nom. 





The price of a carpet 
20010301 

From Amber: i have to calculate the square footage of carpet for me room and im not quite sure how to do that. the carpet is $2.08 per sq. ft. and my room is 12x11ft. Answered by Penny Nom. 





What is my name? 
20010223 

From Julia: My perimeter is 12 cm. My sides are all equal. The sum of half my sides is equal to 6 cm. How many sides do I have? What is my name? Answered by Penny Nom. 





Difference of Squares 
20010222 

From BrunoPierre: I noticed the other day that if you substract two consecutive squared positive numbers, you end up with the same result as if you add up the two numbers. Ex. 5 and 6 (2 consecutive positive numbers) 5^{2} = 25 6^{2} = 36 36  25 = 11 (Substraction of the squared numbers) 5 + 6 = 11 (Sum of the numbers) A more algebric view: a^{2}  b^{2} = a + b where a and b are consecutive positive positive numbers. (b = a + 1) I wondered if this rule had a name, and who discovered it. Answered by Penny Nom. 





Difference of squares 
20010220 

From Janna: Hi! I was just wondering how you would factor x^{2}  9y^{2}. Answered by Harley Weston. 





Finding roots 
20010201 

From A student: My math problem is right now we are working on roots. I don't quite understand how to find the answer to the problems, i was wondering what is the easiest, and fastest way to find the answers to roots? Answered by Penny Nom and Claude Tardif. 





Equilateral 
20010125 

From A student: I AM 9 YEARS OLD AND I HAVE HOMEWORK. I WOULD LIKE TO KNOW IF THERE IS SUCH A THING AS A EQUILATERAL SQUARE. Answered by Penny Nom. 





Square feet and cubic feet 
20010121 

From Jenny: How do I convert square feet to cubic feet? If I have 2000 square feet then how many cubic feet do I have? Answered by Harley Weston. 





Exponents 
20010114 

From A student: I am wondering if a number raised to the second power is "squared" and a number raised to the third power is "cubed" is there a name for any number raised to any other power. Answered by Harley Weston. 





Completing the square 
20010112 

From Jacky Lam: A friend told me that completing square not only can find the vertex but also the roots of a quadratic equation. Is it possible? How? Can you show me how to find the roots of the following equation using completing the square? 8x^{2} + 8x + 4 Answered by Penny Nom. 





Factoring (uv)^{3}+vu 
20001215 

From A parent: I am a middle school teacher and a parent. I am snowed in and trying to help my 9th grader get ready for 9 weeks exams. I have tried to factor this problem to no avail. (uv)^3+vu. I have the answer but I need to know how it is done. Answered by Penny Nom. 





Square roots 
20001029 

From Pamela: HERE GOES(I WILL USE Q AS THE SYMBOL FOR SQUARE ROOT): 8(Q2)  5(Q2) + Q2 SECOND PROBELM IS (1 + Q2)^{2} LAST ONE 3/(2Q5) Answered by Claude Tardif. 





Overlapping a circle and a square 
20001028 

From Jacky: A square with a dimension 20 by 20cm. and a quarter of the circle with the radius of 25cm (A quater of a circle is created by 2 cuts that are perpendicular bisectors of each other where the intersecting point is at the centre of the circle). With these 2 pieces, the 2 pieces are placed over each other in which the 90^{o} angle of the quarter circle matches with one of the right angles on the square. Now, calculate the overlapping area of the 2 figures. Answered by Chris Fisher and Harley Weston. 





The sum of the cubes is the square of the sum 
20001010 

From Otoniel: Without using mathematical induction, or any other method discovered after 1010 a.d. , prove that the sum of i^{3}, (where i, is the index of summation) from one to, n, is equal to ((n*(n+1))/2)^{2} Answered by Penny Nom. 





n^{3} + 2n^{2} is a square 
20000904 

From David Xiao: determine the smallest positive integers, n , which satisfies the equation n^{3} + 2n^{2} = b where b is the square of an odd integer Answered by Harley Weston. 





A equation with a square root 
20000903 

From Lea: Please help with 2 plus the square root ( and under it has x plus 1) = 6 Thank you Answered by Penny Nom. 





The sum of the squares of 13 consecutive positive integers 
20000825 

From Wallace: Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square. Answered by Harley Weston. 





Completing a square 
20000710 

From Lexa Michaels: How do you complete a square? the textbook question is: x^{ 4} + 64 Answered by Penny Nom. 





1+4+9+16+...n^2 = n(n+1)(2n+1)/6 
20000601 

From Shamus O'Toole: How do you derive that for the series 1+4+9+16+25.. that S(n)=(n(n+1)(2n+1))/6 Answered by Penny Nom. 





The square root of 1 
20000519 

From Gary: i am not a student i am just some one that heard something and i can't be sure on the answer...my ? is what is the square root of 1? i think it is 1 but not sure can you let me know please thank you Answered by Harley Weston. 





Circumference = Area 
20000419 

From Scot George: The area and circumference of a circle has the same measurement. Find the radius. Answered by Chris Fisher. 





Factoring trinomials that are squared 
20000417 

From A student: I have a question that I really need an answer to. I need help with factoring trinomials that are squared. Answered by Penny Nom. 





The square root of 3 
20000404 

From Mr. William: Prove that root 3 is irrational Answered by Harley Weston. 





Completing the square 
20000311 

From Sandra: How do i complete the square and leave in simple radical form? x squared + 18x  17=0 Answered by Penny Nom. 





Triangular numbers and square numbers 
20000302 

From Emily McCallum: Would someone find me some math activities using triangular numbers and square number. Especially acitivities that actually form the shapes. They need to be at the 5th grade or 6th grade level. But you can not find anything that can be tauht at these level, that fine. I just need to be able to teach this new subject or kind of math to my kids. Answered by Rick Seaman and Penny Nom. 





Three factors 
20000221 

From A parent: Question from a parent helping a child, grade 4, with homework. Can a number have three factors? Name three numbers that have three factors. Answered by Penny Nom. 





Is a square a rectangle? 
20000215 

From Jaireh: This is something that aroused a debate in class: A rectangle was defined as a parallelogram with 4 right angles. A square was defined as a parallelogram with 4 congruent sides and 4 right angles. I need written and conclusive proof that some rectangles can or cannot be squares. I tried insisting that some of them can.. but without proof nobody will listen. Answered by Walter Whiteley. 





A 4by4 magic square 
20000206 

From Maureen Fitzsimons: I need to create a 4x4 grid using numbers .1, .2, .3, .4, ....1.1, 1.2, 1.3,1.4,1.5,1.6 the sum of the number diagonally, horizontally and across all equal 3.4 Answered by Penny Nom. 





Factoring ^6 
20000103 

From Athena:
my name is Athena and I have a question on factoring: how would you figure this out: (x^{6}y^{6}) and (x^{6}+y^{6}) Answered by Penny Nom. 





An area problem 
19991129 

From Vicky Birch: The length of a rectangle is three times it's breadth. If the length were 6 meters less, and the breadth were 6 meters more, the rectangle would be a square. Make a mathematical model and solve the resulting equation to find the breadth of the original rectangle. What is the area of the square? Answered by Penny Nom. 





Ben's observation 
19991028 

From Emily Nghiem and Ben Rose: As a teacher at a school called Educere in Houston, I have a ninthgrade student who discovered the following shortcut last year as an eightgrader. What he noticed is that given any two consecutive integers (or n and n+1 for any rational number greater than or equal to 2), the difference between their squares was equal to the sum of the two numbers. . .
Answered by Chris Fisher and Penny Nom. 





Calculating a square root 
19991028 

From Jonathan: What is the formula for calculating a square root? Answered by Penny Nom. 





An odd number of factors 
19991022 

From Melissa: What is the common name used for numbers that have an odd number of factors? What is the least positive integer that has exactly 13 factors? Answered by Penny Nom. 





A sum of two squares 
19991008 

From Marksmen: what is the smallest whole number that can be written two ways as a sum of two different perfect squares? i.e.11squared plus 3 squared is 121+ 9=130 and7 squared + 9squared=49 +81= 130. Are there any smaller? I am stumped! Answered by Claude Tardif. 





Magic Square 
19990918 

From Nick Grundberg: Using the this square, fill in the squares using the numbers 1 through 9 just once to make all the sums equal in all directions, across, down, and diagonally. Then tell what the sum of the magic square equals. Answered by Penny Nom. 





2 to the x and x squared 
19990917 

From John: For what values of x is 2 to the exponent x greater than x squared? Answered by Harely Weston. 





Square roots without a calculator 
19990914 

From Josh Weiner: Is there any way to find out a square root without a calculator? Answered by Harley Weston. 





A difference of squares problem. 
19990724 

From Michael and Stephanie Bixler: If you have the equation x= n^{2}  m^{2} (ie 40= 7^{2}3^{2}= 499) x must = a positive number 1) which squared numbers work as n and m 2) how does it work 3) if my teacher gave me the number for x; how could I figure out this problem Answered by Harley Weston. 





The number of acres in a square mile 
19990709 

From Rita Murphy: What is the # of acres in square mile Answered by Harley Weston. 





Introductory Algebra 
19990519 

From Pat: (2 + sq. root of 3) x (2  sq. root of 3) = 1 Please show me the work. Answered by Harley Weston. 





Square feet and acres. 
19990515 

From Helene Freeman: How can I find out about acres in sq. ft. a house lot is 2360 sq. ft. and the house is on 1432 how many acres are left? Answered by Penny Nom. 





An equilateral triangle on a square 
19990426 

From Ed: My Grade 8 class and I were discussing the solution to the following problem: What is the area of the largest equilateral triangle that can be drawn on a 5 cm square. We used 5 cm as the base of our triangle and then drew the other two legs of 5 cm each to make the equilateral triangle. We then drew an altitude from the upper vertex to the base of the triangle. Using the law of Pythagoras with side a of 2.5 and side c of 5 we calculated side b to be 4.3 cm (the altitude). Therefore the area of the triangle would be 5 x 4.3 divided by 2 or 10.75 square cm. The answer key to this resource says I am wrong. What do you think? Have we interpreted the question incorrectly? Answered by Chris Fisher and Harley Weston. 





Universal Area 
19990408 

From Karen Richardson: I need a formula for area that works for a square, a rectangle, a parallelogram, a trapezoid, and a triangle. Answered by Jack LeSage, Chris Fisher and Harley Weston. 





Factoring 
19990330 

From Maggie Stephens: I don't know anything about factoring would you plese help me. 3x^{4}  48 54x^{6} + 16y^{3} 1258x^{3} 12x^{2}  36x + 27 9  81x^{2} a^{3} + b^{3}c^{3} I would greatly appreciate any help you can give me thanks. Answered by Jack LeSage. 





A Frustum 
19990329 

From Monica Armour: What do you call a square pyramid that has had the top chopped off? Answered by Chris Fisher and Jack LeSage. 





Factoring 
19990308 

From L. Sivad: Question: m^{2}+6m+9n^{2} Answered by Penny Nom. 





The square root of two is never supposed to end 
19990306 

From a wondering student: i am algebra II and am in the 9th grade. today we were talking about rational and irrational numbers. When we were talking about square roots my friend and i were talking and we thought of something. if you have a square with sides of length one then the diagonal of the square is the square root of 2. Now the square root of two is never supposed to end. But the diagonal of the square ends so therefore doesn't the square root of 2 end. our math teacher did not really answer our question because it was not in the lesson plan and not to many people would see where we were coming from. the answer is really bugging me and i would like to have your input. Answered by Jack LeSage and Penny Nom. 





Magic Squares 
19990211 

From Katie Powell: My name is Katie Powell. I'm in the 7th grade, taking Algebra. I live in Houston, Texas. My problem is this: "Use the numbers 19 to fill in the boxes so that you get the same sum when you add vertically, horizontally or diagonally." The boxes are formed like a tictactoe  with 9 boxes  3 rows and 3 columns. Can you help? Answered by Jack LeSage. 





The Quadratic Formula 
19990122 

From Eric Morgan: Hi my name is Eric Morgan and I m in 8th Grade honors math (middle) and I'd like to know how to prove the quadratic formula b±sqrt of b(a)(c)over 2(a) Answered by Penny Nom. 





Complex Numbers 
19981223 

From Wayne Bagley: I would like to know what is the square root of i , and i squared? I am looking for a response appropriate for secondary level students. Answered by Harley Weston. 





A tetrahedron inscribed in a cube 
19981118 

From Jane: In analyzing a cube, I would like to find a tetrahedron inscribed in the cube which has none of its faces in the planes of the faces of the cube. I would like to see this tetrahedron outlined in the cube. My name is Jane and my email address is BARSOIAN. I am an elementary education student. Answered by Walter Whiteley. 





Triangular Numbers 
19981030 

From Matt: i would like to know about triangular numbers and it history i would also like to know about the history of prime numbers thank you Answered by Chris Fisher. 





A Six Digit Number 
19981027 

From Craig Bedard: If a certain sixdigit number is split into two parts, one constituting the first three digits and the other the last three digits, and the two parts are added and the resultiong sum squared, it is found that the product is the original six digit number. What is the original sixdigit number? At first it seemed liked an impossible question, until it hit me...how long will it take you? Answered by Jason Stein and Dan Usselman. 





Students and Lockers 
19981002 

From Mike: There is a row of 1000 lockers. There is a line of 1000 students. Student number 1 starts at the first locker and opens all 1000. Student number 2 starts at the second locker and closes every other one. Student number 3 starts at the third locker and goes to every third one, closing the open ones and opening the closed ones. Student number 4 does the same with every fourth locker and so on down the line... After all 1000 students have gone how many lockers are open and which ones are they? Please help! There is proboly a simple solution but we couldnt figure it out for the life of us. Please let us know how you solve it. Answered by Patrick Maidorn and Penny Nom. 





Radicals 
19980915 

From Lana Sabo: Question: fifteen times the square root of twenty, divided by the square root of 2. nine subtract the square root of fortyfive, divided by 3. the square root of 18 plus the square root of 12, divided by the square root of 3. Answered by Harley Weston. 





Difference of squares 
19980623 

From Kristen Smelsky: Solve the following using a difference of squares: 4x(squared) minus 4xy plus y(squared) minus m(squared) plus 2m minus 1 Answered by Penny Nom. 





x^2 = ...444 
19980223 

From James Bauer: What is the first interger that when squared ends in three 4's? (ex. x^2 = ...444) Prove that there are no intergers that when squared end in four 4's (ex. x^2 = ...4444) Answered by Penny Nom. 





The Range of a Function. 
19970912 

From Karel Marek: Math Is Book 6 (Ebos/Tuck) question 5(b) gives a surprising answer at the back of the book..The question is: Indicate the domain and range for this: y = sqr(x9) (Square root of) The answer for the domain is x>=9 which is not surprisingly, but the range is y>=0, yER ... which I could understand if you were not allowed to transform the equation into x as the subject.. But all example on the facing page DO TRANSFORM the equation at will with x and/or y as the subject.. Can you explain this... ?? Answered by Chris Fisher. 





Square Root History 
19970829 

From Carlos Montecel S.: I need find information over the "Square Root History", Could you help me? Answered by Harley Weston. 





Square Roots and Functions. 
19970423 

From Ed: 1. In most texts the solution to a question such as square root x = 6 is x is undefined. Yet when teaching to solve xsquared = 36 x = +6 or 6 There appears to be a contradiction here. My question is when, where and why do we use the principle square root, not both + and ? This often occurs as the extraneous root in the solution of radical equations and in stating the domain and range of functions involving square roots. 2. Are there any simple rules for determining whether equations are functions without graphing them and doing a vertical line test? Answered by Harley Weston. 





Why QUADratic? 
19970319 

From Paula Miller: A student today asked me why a quadratic, with highest power of degree 2, was called a QUADratic. We're awaiting the answer with baited breath! :) Answered by Chris Fisher and Walter Whiteley. 





Approximating roots. 
19961104 

From Ben Dixon: How do you calculate a square root? eg the square root of 2.There is obviously some sort of successive approximation type algorithm for doing it to however many decimal places is required, but what is the algorithm? Answered by Harley Weston. 





Square roots 
19960316 

From Terry King and John: We are just curious about how to manually calculate square roots. Answered by Harley Weston. 





Algorithms for roots 
19960222 

From Charles Hewitt: I have seen an algorithm for finding the square root of numbers. Are there similar such algorithms for higher roots? Answered by Harley Weston. 





Magic Square 
19951020 

From Marianne and Carrie: How can an 8 by 8 square have the same area as a 5 by 13 rectangle? Answered by Denis Hanson. 





racine carrée 
20001124 

From G. Bigorgne: Quel est donc l'origine de l'expression "racine carrée" ? Pourquoi avoir choisi cette expression ? Answered by Claude Tardif. 

