# How do you simplify sqrt 2 / sqrt 10?

$\frac{\sqrt{2}}{\sqrt{10}} = \frac{\sqrt{5}}{5}$
If $a , b \ge 0$ then $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$
$\frac{\sqrt{2}}{\sqrt{10}} = \sqrt{\frac{2}{10}} = \sqrt{\frac{1}{5}} = \sqrt{\frac{5}{25}} = \frac{\sqrt{5}}{\sqrt{25}} = \frac{\sqrt{5}}{5}$
Notice that I chose to make the denominator a perfect square $25$ in order that the final result has a rational denominator.