Simplify square root of -96

$\sqrt{- 96}$

Step 1

Rewrite $- 96$ as $- 1 (96)$ .

$\sqrt{- 1 (96)}$

Step 2

Rewrite $\sqrt{- 1 (96)}$ as $\sqrt{- 1} \cdot \sqrt{96}$ .

$\sqrt{- 1} \cdot \sqrt{96}$

Step 3

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

$i \cdot \sqrt{96}$

Step 4

Rewrite $96$ as $4^{2} \cdot 6$ .

Factor $16$ out of $96$ .

$i \cdot \sqrt{16 (6)}$

Rewrite $16$ as $4^{2}$ .

$i \cdot \sqrt{4^{2} \cdot 6}$

Step 5

Pull terms out from under the radical.

$i \cdot (4 \sqrt{6})$

Step 6

Move $4$ to the left of $i$ .

$4 i \sqrt{6}$