How do you rationalize sqrt(5/8)?

Write it as: $\frac{\sqrt{5}}{\sqrt{8}}$
then multiply and divide by $\sqrt{8}$ to get:
$\frac{\sqrt{5}}{\sqrt{8}} \cdot \frac{\sqrt{8}}{\sqrt{8}} = \frac{\sqrt{5} \sqrt{8}}{8} =$
$= \frac{\sqrt{5} \sqrt{4 \cdot 2}}{8} = 2 \frac{\sqrt{5} \sqrt{2}}{8} = \frac{\sqrt{5} \sqrt{2}}{4} = \frac{\sqrt{10}}{4}$