# Thread: Squaring a square root?

1. ## Squaring a square root?

Hi
Him presented with problems such as

(root x)^4

(root x) ^5

not sure how to solve them since its a root x.

i know that root x ^2 = x but not sure about the other squares. Thanks!

2. ## Re: Squaring a square root?

Originally Posted by minneola24
(root x)^4
(root x) ^5

i know that root x ^2 = x but not sure about the other squares.
That is false: $\displaystyle \sqrt{x^2}=|x|$

But if you have $\displaystyle \sqrt x$ it is assumed that $\displaystyle x\ge 0$.

Thus $\displaystyle (\sqrt x)^4=x^2~\&~(\sqrt x)^5=x^2\sqrt x$

3. ## Re: Squaring a square root?

Originally Posted by Plato
That is false: $\displaystyle \sqrt{x^2}=|x|$

But if you have $\displaystyle \sqrt x$ it is assumed that $\displaystyle x\ge 0$.

Thus $\displaystyle (\sqrt x)^4=x^2~\&~(\sqrt x)^5=x^2\sqrt x$
The OP was correct, since from the context of the question, he/she meant \displaystyle \displaystyle \begin{align*} \left( \sqrt{x} \right)^2 = x \end{align*}.