# Squaring a square root

• February 13th 2010, 05:24 AM
mathemagister
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 $x$ ??
• February 13th 2010, 05:59 AM
Bacterius
Indeed. $\sqrt{x^2} = |x|$ for any $x \in \mathbb{R}$ :)
• February 13th 2010, 06:23 AM
mathemagister
Thanks, Ray. I had only conjectured this, but didn't know if this was true.