







Four consecutive positive integers 
20190312 

From Nabila: The product of four consecutive positive integers in 24024
What is their sum? Answered by Penny Nom. 





A quadratic equation problem 
20190226 

From Em: One root of the equation
2x^2 + bx  24 = 0 is 8. What
are the possible values of b and
the other root? Answered by Penny Nom. 





The exponential form of sqrt(13) 
20190210 

From isaebl: what is the exponential form of sqrt(13) Answered by Penny Nom. 





Fractions with roots 
20190206 

From DEBMALYA: 5/√2+√3 –1/√2–√3 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. 





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. 





Is the square root of 2 plus the square root of 2 irrational? 
20170329 

From haya: how can i prove the the square root of 2 plus the square root of 2 is an irrational number? Answered by Penny Nom. 





Form the quadratic equation which has given roots 
20170116 

From Tharshini: Given a and B are the roots of the quadratic equation x^2+4x+7=0. Form the quadratic equation which has the roots
3a1 and 3B1 Answered by Penny Nom. 





A quadratic equation with equal roots 
20160123 

From abdiwahid: X^2+2ax+4x+9a=0 is quadratic equation which has equal roots. Find the possible value of a? Answered by Penny Nom. 





Find the quadratic equation whose roots are 4 and 7 
20160103 

From sadiya: Find the quadratic equation whose roots are 4 and 7 Answered by Penny Nom. 





The positive root of sin(x) = x^2 
20151213 

From Kemboi: Find the positive root of the equation sin(x) = x^2 Answered by Penny Nom. 





A quadratic equation with known roots 
20151101 

From Awudu: Given the roots of the quadratic equation ax^2+5x+c=0 are 5 and 2/3,find the values of a,b and c. Answered by Penny Nom. 





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. 





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. 





The cube root of 729 
20141112 

From Alexis: What would be the square root of 729 to the third power and could you
explain how to get the answer? Answered by Penny Nom. 





Two quadratic polynomials 
20141028 

From khushboo: The zeroes of a quadratic polynomial x^2+ax+b are 'c' and 'd'
and the zeroes of a quadratic polynomial x^2+cx+d=0 are 'a' and 'b'.
find the numerical value of a+b+c+d where a, b, c and d are non zero integers. Answered by Penny Nom. 





1÷[1√2(order of surd is 4)] 
20140502 

From Anoushka: if t=1÷[1√2(order of surd is 4)] , then t=? Answered by Penny Nom. 





A quadratic equation given the roots 
20140423 

From Sarah: How do you find the quadratic formula when you're given just the roots ... X=3 X= 1/3
Thanks ! Answered by Robert Dawson. 





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. 





Extraneous solutions 
20131022 

From tom: i need an equation where x=2 is the correct answer and x=3 is an extraneous solution. can you provide me with such an equation?? Answered by Harley Weston. 





A quadratic with no real roots 
20130715 

From Pranav: If ax^2+bx5=0 has no real roots. Then d sign of 1) a+b5
2) (25a5b5)(4a+2b5) will be what ?? Answered by Penny Nom. 





Square root 
20121027 

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





Using Newton's Method to find a root 
20120409 

From Nancy: Use Newton's method to find the real root function, accurate to five decimal places
f(x) = x^5+2x^2+3 Answered by Penny Nom. 





A parabolic arch 
20120104 

From Swathi: A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square.
The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch
is 18m.
a)Determine the quadratic function that models that arch
b)State the domain and range of the function 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. 





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. 





The quadratic with two given roots and a constant term 
20110419 

From Lindah: how do I food quadratic with two given roots and a constant term? Answered by Penny Nom. 





Find all the roots 
20101202 

From gagan: find all the roots of z^53z^4+2z^3+z^23z+2 Answered by Stephen La Rocque and Penny Nom. 





z^5  3z^4 + 2z^3 + z^2  3z + 2 
20101106 

From Kumar: would you please solve this problem, related to complex numbers.
Find all the roots of :
z^5  3z^4 + 2z^3 + z^2  3z + 2 Answered by Robert Dawson and Penny Nom. 





A fourth degree polynomial function with real coefficients 
20101030 

From Ryan: Question from Ryan, a student:
What is the fourth degree polynomial function with real coefficients
that has 1,1 and I as zeros and such that f(x)=160 Answered by Harley Weston. 





A polynomial with integer coefficients 
20101023 

From Adori: Question from Adori, a student:
Find a polynomial with integer coefficients that has the given zeros: 2/3, 4, root of 3i, root of 3i. Answered by Harley Weston. 





4√3 + 2√1/3 
20100925 

From Michelle: How do you solve 4√3 + 2√1/3? Please show step by step. Answered by Penny Nom. 





Complex roots 
20100414 

From Lan: If b and c are real numbers so that the polynomial (x^2) + bx + c has 1 + i as a zero, find b + c. Answered by Penny Nom. 





Rational root theorem 
20100414 

From deciree: How could i get the value of x with this equation:
1/13x^3+12x/13=1/2
Thank you! Answered by Harley Weston. 





Factors and zeros of a polynoial 
20100317 

From Susan: find a polynomial function of degree three with 3 as a zero of multiplicity 2 and 4 as a zero of multiplicity 1. Answered by Tyler Wood. 





Zeros of a polynomial 
20100301 

From Gavin: Suppose the polynomial R(x) = a_9x^9+a_8x^8+...+a_1x+a_0 has real coefficients with a_9≠0. Suppose also that R(x) has the following zeros:
2,
3,
i
Using this info, answer the following.
a. What is another zero of R(x)?
b. At most how many real zeros of R(x) are there?
c. At most how many imaginary zeros of R(x) are there?
p.s. I used _ for subscript
thanks so much Answered by Harley Weston. 





The roots of a cubic 
20100121 

From Laura: Consider the equation x^3 + 6x^2  x = 30.
One of the roots is equal to the sum of the other two roots.
Find the values of the three roots. Answered by Chris Fisher and Harley Weston. 





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. 





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. 





Excluded values 
20091114 

From Janie: I have to State the excluded values for this equation and then solve, but not sure how to do this. Here is the problem
(x+6)/x+3=(3)/(x+3)+2 Answered by Harley Weston. 





The roots of a polynomial 
20091103 

From Jess: Find the value of a positive integer k such that f(x)=x^2  2kx + 55 has roots at k +3 and k  3. 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. 





The zeros of a polynomial 
20090925 

From jordan: find a polynomial of lowest degree with only real coefficients and having the given zeros.
1+2i, 2 (multiplicity 2) Answered by Penny Nom. 





Quadratic equations 
20090830 

From jovian: how can i find the quadratic equation of the roots 2/5 and 1/3? Answered by Stephen La Rocque. 





root 2 is irrational 
20090731 

From prateet: prove that root2 is an irrational number. Answered by Robert Dawson. 





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. 





Fractional Exponents 
20090707 

From bob: 2^5/2  2^3/2 Answered by Janice Cotcher. 





Extraneous solutions 
20090602 

From Ayana: solve and check for extraneous solutions.
3x+6/ x²4 = x+1/ x2
x can not = {2,2} Answered by Penny Nom. 





How many times does the graph of y=2xsquared 2x + 3 intersect the xaxis? 
20090527 

From Henry: how many times does the graph of y=2xsquared 2x + 3 intersect the xaxis? Answered by Penny Nom. 





A quadratic equation with roots (4i) and (4+i) 
20090505 

From Kelly: find a quadratic equation with roots (4i) and (4+i) Answered by Harley Weston. 





1/(square root 16) 
20090421 

From Conor: Hi Guys!
I dont have a square root sign so im just gonna use the ^ symbol :)
I am just wondering if
1/(16^a)
when rewritten can it be
1/16 to the power 1/2
Thanks :) Answered by Penny Nom. 





The sum of the roots of a quartic 
20090421 

From dave: This is a algebra problem that i am confused about:
The sum of the roots of x^4x^3+5x^2+4=0 is:
i tried graphing it, but it shows that there are no roots, but the answer is 1. are they wrong? Answered by Penny Nom. 





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. 





Find a polynomial function with the indicated zeros and satisfying the given conditions 
20090323 

From Kristen: Find a polynomial function with the indicated zeros and satisfying the given conditions. Simplofy your answer (no imaginary numbers or parentheses in the answer)
Zeros: 1+2i, 12i, 5 ; f(2)=1 Answered by Harley Weston. 





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. 





ax^2 + bx + c = 0 has no real roots and.... 
20090126 

From Alberto: The equation ax^2 + bx + c = 0 has no real roots and a + b + c < 0 . Chose the right answer:
(A) c > 0
(B) c <= 0
(C) c = 0
(D) c >= 0
(E) c < 0
Explain the choice. Answered by Robert Dawson and Harley Weston. 





The sum of the roots of a quartic 
20090103 

From peter: How do you find the roots of an equation without graphing? like, i have a problem that says what is the sum of the roots of x^4x^3+5x^2+4=0. Answered by Harley Weston. 





The square root of 164 
20081231 

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





Factor 9x^2 + 6x + 4 
20081121 

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





An equation with three radicals 
20081113 

From Crystal: I need to solve this radical equation but i am confused on how to solve it with three square roots in it.
sqrt(3x)+3sqrt(2x3)=sqrt(3x2) Answered by Harley Weston. 





Equations with fractional powers and roots 
20081112 

From David: Find all real solution to each equation.
x^2/3 = 9 how do you do this if its to the power
x + 1= Square root (3x +13) can you explain how to get an solution with square root? 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. 





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. 





The cube root of a really big number 
20080717 

From Pete: Is the only way to find a cube root of a really big number guess and check, as i read in other questions, or is there another way without a calculator? Answered by Harley Weston. 





Sum and product of the roots of a quadratic 
20080703 

From Gautam: If a and b are the roots of x^2+px+1=0 and c and d are the roots of
x^2+qx+1=0
prove that
(ac)(bc)(a+d)(b+d)=q^2p^2
Regards
Gautam Answered by Harley Weston. 





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. 





The positive real zeros of f(x) = x^4 + x^3  7x  1 
20080606 

From CiCi: How many positive real zeros does the function f(x) = x4 + x3  7x  1 have? Answered by Janice Cotcher and Harley Weston. 





A quadratic equation 
20080603 

From Drew: A solution of x^28x=17 is
4 or 4+I or 4 or 4+i Answered by Janice Cotcher. 





A root of a polynomial 
20080503 

From john: here is a word problem that my teacher gave us to do can you help me understand it
Give possible formulas (in factored form) and sketch the graphs for two different polynomials that have roots 3, 1, and 2, but cross the xaxis only at x=2 and have yintercept 4.5. What is the lowest degree such a polynomial can have? Can it have an even degree? An odd degree? Explain why.
her term "root" has completely thrown me off, i've reviewed my book and cant find what she is referring to. can anyone help? Answered by Penny Nom. 





For what values of a does x^313x+a have 3 distinct roots? 
20080425 

From Jyotishman: What can be the value of a for the equation to have 3 roots?
x^313x+a=0 Answered by Harley Weston. 





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. 





Find the quadratic equation with roots at (3i) and its complex conjugate 
20080422 

From Tiffany: Find the quadratic equation with roots at (3i) and its complex conjugate. 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. 





The cube root of 198 
20080327 

From bobby: what is the cubed root of 198 Answered by Harley Weston. 





The product of the roots 
20080319 

From Rebecca: Determine the product of the roots of the equation
(x1)(x2) + (x2)(x5)=0 Answered by Penny Nom. 





The sum and product of the roots of a quadratic 
20080316 

From Katelyn: Write the quadratic equation....
Sum of the roots = 16
Product of the roots = 80 Answered by Penny Nom. 





Estimate the cube root of 270 
20080311 

From Tom: (a) By plotting suitable graphs, estimate to one decimal place the cube root of 270.
(b) With reference to your answer to part (a), use 8 iterations of a Bisection Search to refine your estimate. Use the nearest whole numbers either side of your estimate from part (a) as starting values.
(c) Using either of your starting values from part (b) as first guess, use the NewtonRaphson method to find the true value of the root (to 6 decimal places). Repeat using the other starting value from part (b) and compare the two results. Answered by Harley Weston. 





The cube root of 103163 
20080212 

From jeff: find the cube root of 103163 Answered by Stephen La Rocque and Harley Weston. 





Graphing a parabola 
20080116 

From Sean: How do I find the roots and describe the roots when graphing a parabola?
y =  x^2  4x 3 Answered by Stephen La Rocque. 





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. 





The rational root theorem 
20071209 

From Josh: Prove the rational root theorem (where, in a polynomial equation, all
factors of the constant divided by all factors of the leading coefficient
are possible rational roots of the equation). Answered by Penny Nom. 





Imaginary roots 
20071209 

From Josh: What is the correlation between imaginary roots (of a quadratic or other
polynomial equation) and the graph of the equation? As in, how can one
represent imaginary solutions graphically (and why does that work)? Answered by Harley Weston. 





14/square root 3 
20070912 

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





Does every number have a square root? 
20070910 

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





Simplify (square root of)200 
20070828 

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





What feature on a graph shows the solution? 
20070819 

From San: To solve the equation 2sinx+square root 3=0, what feature of the graph,
in the form y=asinx+b would show the solution? Draw a graph to show
the solution. thanks. Answered by Stephen La Rocque. 





The roots of (x  k)(13x) + 1 = 0 
20070628 

From Claire: Show that the roots of (x  k)(13x) + 1=0 are real and distinct for all real values of k. Hence, or otherwise, find the range of 9sin^2 r  6sin r + 13 Answered by Harley Weston. 





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 the equation given three roots 
20070521 

From Aydee: 1. find the equation for the roots given: 7,5,2
2. find the equation for the roots given: 5,2+sqrt3,2sqrt3 Answered by Penny Nom and 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. 





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. 





x^3  3kx + 1 = 0 
20070311 

From Sandra: Show that x^3  3kx + 1 = 0 does not have two distinct roots when k < 0. Answered by Stephen La Rocque and Penny Nom. 





Finding the xintercept 
20070302 

From Ash: Y = 1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT Answered by Gabriel Potter. 





The cube root of 8000 
20070131 

From Jacqui: How would you find the answer of a cube root backwards. For example: 8000 but backwards. Like, what number made that and how would you do it? 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. 





Prove that square root of 3 is irrational. 
20061221 

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





The roots of a quadratic equation 
20061116 

From Lana: If p and q are the roots of 2X^2 +3X+7=0, compute pq^3+qp^3. thanks for your help. Answered by 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. 





Is this unsolvable? 
20060919 

From Al: Is this unsolvable???
2xy + 3x^2  3y + y^3 = 4x + 3 where y=3. Answered by Penny Nom and Claude Tardif. 





Square roots in a binomial expansion 
20060911 

From Sydney: (√x + 5)^{4} expanded using the binomial theorem 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. 





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. 





Square roots 
20060307 

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





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. 





Quadratic Equations & Given Roots 
20051111 

From Lindsey:
I need to find the quadratic equation in the form:
f(x)=a(x^{2}  (b/a)x + (c/a))
The vertex is (1, 7), the roots are (4, ?)
I need to find the other root but I don't know where to begin. My answer key says the other root is (2). How is this possible?
Answered by Penny Nom. 





ax+b = cx + d 
20050322 

From Angel:
ax+b = cx + d
how to show sometimes the above has 2 roots, sometimes 1 root and sometimes
no roots. Hopelessly lost on how to start...
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. 





Factoring a cubic 
20050220 

From Abraham: How would you factor completely,
x^{3}x^{2}+5x5? Answered by Claude Tardif. 





Solve for x 
20050202 

From Christie: Solve for x
.387 = (.40  .265x)/(sqrt(1x2)) Answered by Penny Nom. 





Imaginary roots of a ploynomial 
20041031 

From Jennifer: how to find the roots of a polynomial equation if it would be imaginary? Answered by Harley Weston. 





Cube roots 
20041026 

From A parent: How do you solve the problem of finding the cubed root of (17 to the power of 3).
Can you show me each step and if you have a visual representation of this it would be very helpful.
Also can you show a step by step of finding the cubed root of 27. Visuals help a lot 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. 





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. 





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. 





Evennumbered roots 
20040301 

From A student: I understand that the square root is defined to be positive only. Does
the same rule apply to other evennumbered roots, such as the 4th root, or
the 6th root, etc.? Answered by Harley Weston. 





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. 





Polynomials degree 4 and bigger 
20030626 

From Stephen:
How do I show kids how to find all the zeros for polynomials degree 4 and bigger.
For examples: r(x) = x^{5}11x^{3}7x^{2}+77 = (x^{2}11)(x^{3}7) and s(x) = x^{4}121 = (x^{2}11)(x^{2}+11) Also am I correct when I say that the following are irreducible? f(x) = x^{2}11 g(x) = x^{3}7 h(x) = x^{4}5 Answered by Harley Weston. 





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. 





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. 





Extraneous solutions 
20030124 

From Paul:
What is an extraneous solution and in what cases do you get one? How do you know it is extraneous? Answered by Penny Nom. 





Quadratic equations 
20021210 

From Katie: just bugging the hell outta me and I cannot figure it out for the life of me.
1)x2x1 =0 Find both roots. You must simplify both of your roots. This equation requires the use of the Quadratic Formula. I have tried everything for this and I am still either getting the wrong answers, and end up getting really frustrated. If you could find the answers and tell me how you did it I would greatly appreciate it! Then the second problem is
2) The square of a certain negative number is equal to 70 decreased by 3 times the number. Find the answer! On this one I set it up but still came out with the wrong answer. So if you could help me on this one I would greatly appreciate it! Answered by Penny Nom. 





Factoring a cubic 
20021205 

From Dorota: I got a problem with factorise the expression 2x^{3}+11x^{2}5x50. 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. 





A polynomial 
20020414 

From A student: A polynomial function is described by the following conditions: f(x) has two real zeros at x= 2 and x= 1, each of multiplicity 2 f(x) has two complex zeros as x goes to infinity, f(x) goes to +infinity as x goes to +infinity, f(x) goes to +infinity f(x) has a yintercept at (0,2) Sketch a polynomial function that satisfies the above conditions. Write an equation for function f(x) Write another function g(x) that also satisfies the above parameters. 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. 





Cube roots 
20020326 

From Kathy: My son is in 4th grade and needs to simplify the cube roots of 216, 512 and 64. How does he do this with a regular calculator or without? 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. 





A degree 5 polynomial 
20020217 

From Carla: Write an equation for a polynomial of degree 5 given the following zeros: 7+3i, 2+sqrt(13), 6 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. 





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. 





Some irrational numbers 
20010703 

From Kellie:
 Is it possible to write pi as a fraction?
 Is it possible to write the square root of 2 as a fraction.. Explain why?
Answered by Harley Weston. 





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. 





25 y^2 + 20 y z  4 z^2 
20010515 

From Kimmy: i don't know how to factor the trinomial 25y^{2} + 20yz  4z^{2}. I can get it, but i get messed up on getting the minus 4 at the end. all i get is a plus 4. Can it even be factored. Answered by 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. 





Cube roots on a calculator 
20010324 

From Will: Hi my name is Will.I have a question about the calculator TI83 Plus or the use of a scientific calculator. It is about using them to turn a cubed root to a decimal. When using that for a rational and irrational number. Rational numbers is a number that terminates or repeates. A irrational number goes on and on and uses ... (like pie). Like when you type the cube root of 8 it gives you 2, and that is a rational number. The squre root of 2 is 1.41421356... that is irrational. So why is it when you put the cube root of 16 in the calculator it says 2.5198421 that is rational it terminates at the ninth digit and my float is set for the tenth? But why when you do it by hand you get the 2 times the cube root of 2 and that is irrational? Why is that? Answered by Judi McDonald. 





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. 





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. 





The solutions of a quadratic 
20010130 

From A student:
 Show that the product of the solutions of ax^{2} + bx + c = 0 is c/a.
 For each equation under the given condition, (a) find k and
(b) find the other solution. kx^{2}  2x + k = 0; one solution is 3 Answered by Penny Nom. 





Some complex problems 
20010115 

From Nick: I am having enormous difficulty with one question in my maths homework. The question is shown below. If anybody out there can find the answers and show the workings and help me to understand. 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. 





An infinite series 
20001216 

From John: summation(n=1 to infinity)[n sin(1/(2n))]^{n} Answered by Harley Weston. 





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. 





Roots of x^2 + 22 x + 112 
20000907 

From Brian R.: I need to find the root of the quadratic equation of a square. The problem is x^{2} + 22x + 112 = 0. Answered by Penny Nom. 





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 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. 





Graphing cube roots 
20000427 

From Heather Jones: What do the graphs of cube roots look like? Answered by Walter Whiteley. 





Finding a Quadratic Equation given the roots 
20000416 

From A secondary student: How do I find the equation for the quadratic with roots at 2i and its complex conjugate? Answered by Harley Weston. 





All the roots of x^6  64 
20000415 

From Dakota: Find ALL zeros of P(x) = x^{ 6}  64 Answered by Walter Whiteley. 





The square root of 3 
20000404 

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





root(1)* root(1) 
20000320 

From Michael Moran: i squared = 1 but i squared = root(1)* root(1) = root( 1*1) = root(1) = 1 1 doesn't = 1 can you help me with my question Answered by Claude Tardif. 





Irrational algebraic functions 
20000221 

From Bucky Cadena: Here is the multipart problem: Given f(x) = x3* squareroot of x + 4 What does the f(x) intercept equal Find the two values for which f(x) = 5 Find the one value for which f(x) = 3 Answered by Harley Weston. 





Complex Roots 
20000124 

From Jess Rutherford: How do I find the value of k when 5x^{2} + k = 3x and has complex roots ? Answered by Penny Nom. 





Calculating a square root 
19991028 

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





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. 





Spreading a rumor 
19990913 

From Bornstar14: There is someone who wants to spread a rumor within 7 days to 250,000,000 people. he wants to know how many people he should tell on the first day (assuming the rumor is passed by everyone who was told to the same amount of people) so that everyone knows on the 7th day. What I did is the 7th root of 250,000,000. this answer is not possible unless rounded. is it okay for the number to be approximate? 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. 





Simplifying Radicals 
19990126 

From Mary: I would like to know how to simplify this question:
4 __________________ squareroot7 + squareroot3
I know the answer is (sqrt7  sqrt3) but i would really love to know how to get that answer!! Thanks. Answered by Jack LeSage and Penny Nom. 





Simplifying Radicals 
19990125 

From Randy: Find the perimeter of a rectangle in simplified radical form L=root80 W=root45. I would appreciate a detailed explination of the process for solving. Answered by Jack LeSage and Penny Nom. 





Root 17 is Irrational 
19990121 

From John Murdock: If you could help me out with this I would appreciate it. Prove that the square root of 17 is irrational. Answered by Harley Weston. 





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. 





Simplifying Roots 
19980918 

From Lauren Lattimer: 1. 2root27 divided by root 12 2. 3 root 48root 75 Answered by 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. 





The Factor Theorem 
19980118 

From Dhruv Bansal: Hi, I'm a ninth grade student doing a math project for school. I'm trying to learn about various ways of solving 3rd and 4th degree polynomial equations using the remainder theorem, the factor theorem, and synthetic division. The books I have all mention x  r, which I know nothing about, not even how to get it. I would really appreciate any information on this. Thanks. Dhruv Bansal Answered by Penny Nom. 





Multiplying imaginary numbers. 
19971103 

From Jim Catton: Here is the question: (square root 2) x (square root 8) My algebra suggests two possibilities . . .
Answered by Walter Whiteley, Chris Fisfer and Harley Weston. 





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. 





Roots of a Polynomial 
19961206 

From Paula Miller: Why is the solution called a "root"? Why not just the "xintercepts"? Answered by Chris Fisher and Harley Weston. 





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. 





The impossible problem 
19960315 

From Shaun Reynolds and Jacob Hiatt: How do you solve (the 6th root of x)+4=3? Answered by Penny Nom and Maxine Stinka. 





Cardano's method 
19960311 

From Mike Gorski: What is Cardano's method for finding the roots of a cubic equation? 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. 





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. 

