# Squaring a square root?

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• December 3rd 2012, 03:15 PM
minneola24
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!
• December 3rd 2012, 03:32 PM
Plato
Re: Squaring a square root?
Quote:

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

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

Thus $(\sqrt x)^4=x^2~\&~(\sqrt x)^5=x^2\sqrt x$
• December 3rd 2012, 04:30 PM
Prove It
Re: Squaring a square root?
Quote:

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

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

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

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