Answer
$\frac{1}{3}$
Work Step by Step
$\frac{\sqrt -8}{\sqrt -72}=\frac{i\sqrt 8}{i\sqrt 72}=\frac{i}{i}\times\frac{\sqrt 8}{\sqrt 72}=1\times\sqrt \frac{8}{72}=\sqrt \frac{8}{72}=\sqrt \frac{1}{9}=\frac{1}{3}$
We know that $\sqrt \frac{1}{9}=\frac{1}{3}$, because $(\frac{1}{3})^{2}=\frac{1}{9}$.
We know that $\sqrt -1=i$, because $i^{2}=-1$.