Simplify ( square root of -12)/( square root of 6)

$\frac{\sqrt{- 12}}{\sqrt{6}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 12$ as $- 1 (12)$ .

$\frac{\sqrt{- 1 (12)}}{\sqrt{6}}$

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{12}}{\sqrt{6}}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{i \cdot \sqrt{12}}{\sqrt{6}}$

Step 2

Combine $\sqrt{12}$ and $\sqrt{6}$ into a single radical.

$i \cdot \sqrt{\frac{12}{6}}$

Step 3

Divide $12$ by $6$ .

$i \sqrt{2}$