Answer
$\frac{1}{2}$
Work Step by Step
$\frac{\sqrt -10}{\sqrt -40}=\frac{i\sqrt 10}{i\sqrt 40}=\frac{i}{i}\times\frac{\sqrt 10}{\sqrt 40}=1\times\sqrt \frac{10}{40}=\sqrt \frac{10}{40}=\sqrt \frac{1}{4}=\frac{1}{2}$
We know that $\sqrt \frac{1}{4}=\frac{1}{2}$, because $(\frac{1}{2})^{2}=\frac{1}{4}$.
We know that $\sqrt -1=i$, because $i^{2}=-1$.