Evaluate square root of -162

$\sqrt{- 162}$

Step 1

Rewrite $- 162$ as $- 1 (162)$ .

$\sqrt{- 1 (162)}$

Step 2

Rewrite $\sqrt{- 1 (162)}$ as $\sqrt{- 1} \cdot \sqrt{162}$ .

$\sqrt{- 1} \cdot \sqrt{162}$

Step 3

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

$i \cdot \sqrt{162}$

Step 4

Rewrite $162$ as $9^{2} \cdot 2$ .

Factor $81$ out of $162$ .

$i \cdot \sqrt{81 (2)}$

Rewrite $81$ as $9^{2}$ .

$i \cdot \sqrt{9^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$i \cdot (9 \sqrt{2})$

Step 6

Move $9$ to the left of $i$ .

$9 i \sqrt{2}$