Question

Why is \displaystyle \sqrt{x^2} = |x|

but \sqrt{4} = 2

rather than \sqrt{4} = |2|

Answer 1

Well, |2| = 2.
Try to understand it like this:\[\sqrt{(-2)^2}\ne -2\]But\[\sqrt{(-2)^2} = \sqrt{4} = |- 2|\]So what this equation is actually saying is that you cannot simply cancel out the square root and square. You have to consider the sign of the thing too.

Answer 2

Also it works for positive numbers\[\sqrt{2^2} = |2 | = 2\]