My Math Forum What are square roots for?

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 March 15th, 2009, 08:47 PM #1 Newbie   Joined: Mar 2009 Posts: 3 Thanks: 0 What are square roots for? I apologize for the simplicity of the question. I have young kids at home studying math and they can't seem to answer this question satisfactorily. From my statistics classes, I know that the square root of the variance gives you the standard deviation--a linear measurement value. So, what do square roots do? What are they good for? In simple terms, if at all possible. Thanks so much for humoring me on this.
 March 15th, 2009, 11:06 PM #2 Member   Joined: Mar 2009 From: San Bernardino, California Posts: 50 Thanks: 0 Re: What are square roots for? Square roots are the inverse operation of squaring a number. It simply is the reversal of squaring a number and this is true for all n-th root operations--it reverses the act of raising the original number, variable, or expression to the nth power. It is similar of how subtraction reverses addition and division reverses multiplication. Once it is developed as a basic arithmetic function it is used in all sorts of ways in math. For example with out the square root function solving this would take much longer by having to expand each binomial quantity: $(3x+2)^2=(x^2+4)^2$ Taking the square root of both sides of the equations allows us to avoid expansion: $3x+2=x^2+4$ $x^2-3x+2=0$ $(x-1)(x-2)=0$ $x=${1,2} Expanding would take much longer.
 March 16th, 2009, 12:12 AM #3 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: What are square roots for? Square roots are used to calculate the length of the diagonal of a rectangle. If the sides of a rectangle measure x and y, the diagonal is $\sqrt{x^2+y^2}$. Square roots are used to calculate the side length of a square. If 16 square tiles are arranged as a square, it must be 4x4, because 4 is the square root of 16. Square roots let you split a multiplication in half. If a plant grows faster the bigger it gets, and if it takes two weeks for a plant to get nine times bigger, you could estimate that after one week it was three times bigger.
 March 16th, 2009, 06:13 AM #4 Senior Member   Joined: Sep 2008 Posts: 116 Thanks: 0 Re: What are square roots for? Best way I can think to explain it is this: Every function has/needs to have an inverse. Square roots are simply the inverse of a square. Without square roots you could never take the inverse of a squared function.
 March 16th, 2009, 08:20 AM #5 Newbie   Joined: Mar 2009 Posts: 3 Thanks: 0 Re: What are square roots for? Fabulous. Thanks for taking the time. You seem to speak a different language than me, yet so common to each of you. I used to think I was strong in Math. But now that I'm old, I seem to have forgotten most of it. Keep the explanations coming...I'll probably have to look up what some of it means (like functions).
 March 16th, 2009, 08:24 AM #6 Newbie   Joined: Mar 2009 Posts: 3 Thanks: 0 Re: What are square roots for? By the way, how many of you celebrated Square Root Day on March 3? (http://news.yahoo.com/s/ap/20090303/ap_ ... e_root_day) Come on. Don't be embarrassed. Raise your hand if you did--or even thought about it.
March 16th, 2009, 11:07 AM   #7
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Re: What are square roots for?

Quote:
 Originally Posted by romeroom By the way, how many of you celebrated Square Root Day on March 3? (http://news.yahoo.com/s/ap/20090303/ap_ ... e_root_day) Come on. Don't be embarrassed. Raise your hand if you did--or even thought about it.
I can't say I celebrated it, but it was brought to my attention by my girlfriend (she's also a Math Major, ). She called is squre'day though, not square root'day, close enough.

 March 17th, 2009, 01:53 PM #8 Senior Member   Joined: Jul 2008 Posts: 895 Thanks: 0 Re: What are square roots for? Given the area of a square, the square root is the length of the side. Asking what it is for is too broad a question. It has multiple uses, as will be discovered throughout further study. It's like asking what is three times a number useful for? It is just another number that has characteristics that are useful. It is an extension of exponents 8^3 = 512, 8^2 = 64, 8^1 = 8, 8^0 = 1, 8^-1 = 1/8, 8^-2 = 1/64, 8^-3 = 1/512. Now, what about exponents that are not integers such as 3, 3, 1, 0, -1, -2, -3, ...? What about fractions? They are just as good is seems, as can be found in more advanced study. So, 16^(1/2) is the square root of 16. 8^(1/2) is irrational, but again just as good a number as any other Real number. Each has a place on the Real number line. Ask the child to be patient, and be patient yourself. You must crawl before you walk, before you run.

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