Evaluate - square root of -72

$- \sqrt{- 72}$

Step 1

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

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

Step 2

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

$- (\sqrt{- 1} \cdot \sqrt{72})$

Step 3

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

$- (i \cdot \sqrt{72})$

Step 4

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$- (i \cdot \sqrt{36 (2)})$

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

$- (i \cdot \sqrt{6^{2} \cdot 2})$

Step 5

Pull terms out from under the radical.

$- (i \cdot (6 \sqrt{2}))$

Step 6

Simplify the expression.

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

$- (6 \cdot i \sqrt{2})$

Multiply $6$ by $- 1$ .

$- 6 i \sqrt{2}$