Is Sqrt(x^2) Always Equal to |x|?

[TyErd]

Okay, when I enter into the calculator sqrt(x^2) it equals |x|. Since when? I thought sqrt(x^2) equals x and then when you go to sketch it, it will be a positive diagonal line through the origin whereas |x| is a reflection at the origin.

 

[Jebus_Chris]

A number squared is always positive. So if you plug in -10 you get sqrt(100) which is 10.
When you cancel out the square and the square root in a problem you do that because you're looking for the principle root aka the positive one.