In what way issquaringthe inverse ofsquare rootsor is it vice-versa?

Our teacher said that they are inverses of each other but did not explain why.

The first word in the title of this post should be Squaring NOT Suare...spelling error.

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- Aug 1st 2008, 02:31 AMmagentaritaSuare Roots and Squaring
In what way is

**squaring**the inverse of**square roots**or is it vice-versa?

Our teacher said that they are inverses of each other but did not explain why.

The first word in the title of this post should be Squaring NOT Suare...spelling error. - Aug 1st 2008, 03:21 AMnikhil
Let f(x)=y=x^2 then

x=y^(1/2)

or f^-1(x)=x^(1/2)

we only consider positive root otherwise result will be a relation not function.

Hope this helps - Aug 1st 2008, 05:06 AMTKHunny
Think long and hard on these two statements:

$\displaystyle \left(\sqrt{x}\right)^{2} = x$

$\displaystyle \sqrt{x^{2}} = |x|$ - Aug 1st 2008, 05:20 AMmagentaritaTKHunny
I thank both of you.

TKHunny:

I understand why [sqrt{x}]^2 = x but I do not understand what the absolute value of x or |x| has to do with

sqrt{x^2}.

What's the connection in the second case?

Thanks - Aug 1st 2008, 10:43 AMmasters

http://www.mathhelpforum.com/math-he...f46463d2-1.gif

In this case Rita,could very well be a negative number. So, to make sure that you obtain the positive principal root, you must take the absolute value.**x**

Just remember this. If you take anof any variable raised to any power and the resulting variable has an**even root**power, you must take the absolute value of the variable.**odd**

Example:

$\displaystyle \sqrt[4]{16x^5y^6z^8}=2|xy|z^2\sqrt[4]{xy^2}$ - Aug 2nd 2008, 06:24 AMmagentaritaI get it...
I get it now.

Thanks