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Math Help - Squaring a square root?

  1. #1
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    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!
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  2. #2
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    Re: Squaring a square root?

    Quote Originally Posted by minneola24 View Post
    (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
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  3. #3
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    Re: Squaring a square root?

    Quote Originally Posted by Plato View Post
    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*}.
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