Evaluate ( square root of -72)/( square root of 6)

$\frac{\sqrt{- 72}}{\sqrt{6}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 72$ as $- 1 (72)$ .

$\frac{\sqrt{- 1 (72)}}{\sqrt{6}}$

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{72}}{\sqrt{6}}$

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

$\frac{i \cdot \sqrt{72}}{\sqrt{6}}$

Step 2

Combine $\sqrt{72}$ and $\sqrt{6}$ into a single radical.

$i \cdot \sqrt{\frac{72}{6}}$

Step 3

Divide $72$ by $6$ .

$i \cdot \sqrt{12}$

Step 4

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$i \cdot \sqrt{4 (3)}$

Rewrite $4$ as $2^{2}$ .

$i \cdot \sqrt{2^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{3})$

Step 6

Move $2$ to the left of $i$ .

$2 i \sqrt{3}$