# How do you simplify: Square root of 1/16?

$\frac{1}{4}$
$\sqrt{\frac{1}{16}} = \frac{1}{4}$ since ${\left(\frac{1}{4}\right)}^{2} = {1}^{2} / {4}^{2} = \frac{1}{16}$
In general, given $a > 0$, the symbol $\sqrt{a}$ represents the unique positive number whose square is $a$: ${\left(\sqrt{a}\right)}^{2} = a$. Proving that it exists and is unique is very difficult, in general, however. It requires a class called "real analysis".