Evaluate square root of -216

$\sqrt{- 216}$

Step 1

Rewrite $- 216$ as $- 1 (216)$ .

$\sqrt{- 1 (216)}$

Step 2

Rewrite $\sqrt{- 1 (216)}$ as $\sqrt{- 1} \cdot \sqrt{216}$ .

$\sqrt{- 1} \cdot \sqrt{216}$

Step 3

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

$i \cdot \sqrt{216}$

Step 4

Rewrite $216$ as $6^{2} \cdot 6$ .

Factor $36$ out of $216$ .

$i \cdot \sqrt{36 (6)}$

Rewrite $36$ as $6^{2}$ .

$i \cdot \sqrt{6^{2} \cdot 6}$

Step 5

Pull terms out from under the radical.

$i \cdot (6 \sqrt{6})$

Step 6

Move $6$ to the left of $i$ .

$6 i \sqrt{6}$