Answer
$-\sqrt{2}i=0-\sqrt{2}i$
Work Step by Step
$\displaystyle \frac{\sqrt{-36}}{\sqrt{-2}\sqrt{-9}}=\frac{6i}{\sqrt{2}i* 3i}=\frac{2}{\sqrt{2}i}=\frac{2}{\sqrt{2}i}*\frac{\sqrt{2}i}{\sqrt{2}i}=\frac{2\sqrt{2}i}{2i^{2}}=\frac{\sqrt{2}}{i}=\frac{\sqrt{2}i}{i*i}=\frac{\sqrt{2}i}{-1}=-\sqrt{2}i=0-\sqrt{2}i$