1. 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.

2. 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

3. Think long and hard on these two statements:

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

$\displaystyle \sqrt{x^{2}} = |x|$

4. 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

5. 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

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:

$\displaystyle \sqrt[4]{16x^5y^6z^8}=2|xy|z^2\sqrt[4]{xy^2}$

6. I get it...

I get it now.

Thanks