<s>[INST] Is $\sqrt{x^2} = (\sqrt x)^2$? Take $x=4$ for example:
$ \sqrt{(4)^2} = \sqrt{16} = \pm4 $
However:
$ (\sqrt{4})^2 = \sqrt{\pm2}$ 
Case 1: $ (-2)^2 = 4$ 
Case 2: $ (2)^2 = 4$
Solution : $+4$
How come the $ \sqrt{(4)^2} = \pm4$; but $ (\sqrt{4})^2 = 4 $ ? 
What is missing?
 [/INST] In general:
$$\sqrt{x^2}=|x|\implies \sqrt{x^2}=\left(\sqrt{|x|}\right)^2=|x|$$
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