Thread: 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).

for all

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?

for all ??

Indeed. for any

Thanks, Ray. I had only conjectured this, but didn't know if this was true.