







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. 





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. 





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. 





Square root 
20121027 

From Ashley: what does square root means 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 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. 





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. 





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. 





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. 





The square root of 164 
20081231 

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





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 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





The square root of 3 
20000404 

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





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. 





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. 





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 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. 





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. 





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. 

