Simplify 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

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

$6 i \sqrt{2}$