Do you take the negative square root when you raise a number to the power of a half?

Question

E.g. does $4^{1/2} = \pm 2$ and if not, why?

Answer 1

$\sqrt{4}=2$ not $-2$ because the range of $f(x)=\sqrt{x}$ $x\in[0,\infty)$ is $[0,\infty)$ therefore $4^{1/2}=2$

Also $\sqrt{(2)^2}=\vert 2 \vert =2$ And $\sqrt{(-2)^2}=\vert -2 \vert =2$ So $\sqrt{4}=2$