Answer
$\frac{1}{3}$
Work Step by Step
Step 1: $\frac{\sqrt (-20)}{\sqrt (-180)}$
Step 2: $\frac{\sqrt (-1\times20)}{\sqrt (-1\times180)}$
Step 3: $\frac{\sqrt (-1)\times\sqrt 20}{\sqrt (-1)\times\sqrt (180)}$
Step 4: Removing $\sqrt (-1)$ as it is common to both numerator and denominator, $\frac{\sqrt (20)}{\sqrt (180)}$
Step 5: $\frac{\sqrt (20)}{\sqrt (180)}=\frac{\sqrt (20)}{\sqrt (20\times9)}=\frac{\sqrt (20)}{\sqrt (20)\times\sqrt 9}$
Step 6: Removing $\sqrt (20)$ as it is common to both numerator and denominator, $\frac{1}{\sqrt (9)}$
Step 7: $\frac{1}{\sqrt (9)}=\frac{1}{3}$
