# Suare Roots and Squaring

• Aug 1st 2008, 02:31 AM
magentarita
Suare 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 AM
nikhil
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 AM
TKHunny
Think long and hard on these two statements:

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

$\sqrt{x^{2}} = |x|$
• Aug 1st 2008, 05:20 AM
magentarita
TKHunny
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 AM
masters
Quote:

Originally Posted by magentarita
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

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

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

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

Example:

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

Thanks