# Does 1 over square root 2 equal square root 1/2?

$\frac{a}{\sqrt{2}} =$ you can take the root of the numerator (which in this case is $a = 1$) but you have always to square it (to avoid changing your fraction) so you get:
$\frac{\sqrt{{a}^{2}}}{\sqrt{2}}$ you can use one square root only:
$= \sqrt{{a}^{2} / 2} =$ but in this case $a = 1$ so that ${1}^{2} = 1$ so you get $= \sqrt{\frac{1}{2}}$