Answer
$\frac{i}{2}$
Work Step by Step
Step 1: $\frac{\sqrt (-2)}{\sqrt 8}$
Step 2: $\frac{\sqrt (-1\times2)}{\sqrt (2\times4)}$
Step 3: $\frac{\sqrt (-1)\times\sqrt 2}{\sqrt 2\times\sqrt 4}$
Step 4: Removing \sqrt 2 as it is common to both numerator and denominator, $\frac{\sqrt (-1)}{\sqrt 4}$
Step 5: $\frac{i}{2}$
