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Math Help - Squaring a square root

  1. #1
    Member mathemagister's Avatar
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    Squaring a square root

    I realize that a variable expression or just a variable that is squared and square rooted cannot be simplified to the expression itself (due to negation of negatives after squaring).

    \sqrt{x^2}\neq x for all  x<0

    I logically thought about this and came to the conclusion that this the square of a square root of an expression must be the absolute value of the expression. Is this true?

    \sqrt{x^2} = |x| for all  x ??
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  2. #2
    Super Member Bacterius's Avatar
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    Indeed. \sqrt{x^2} = |x| for any x \in \mathbb{R}
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  3. #3
    Member mathemagister's Avatar
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    Thanks, Ray. I had only conjectured this, but didn't know if this was true.
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