#### Answer

$\sqrt 3$

#### Work Step by Step

$\frac{\sqrt -300}{\sqrt -100}=\frac{i\sqrt 300}{i\sqrt 100}=\frac{i}{i}\times\frac{\sqrt 300}{\sqrt 100}=1\times\sqrt\frac{300}{100}=\sqrt\frac{300}{100}=\sqrt 3$
We know that $\sqrt -1=i$, because $i^{2}=-1$.