Evaluate square root of -192

$\sqrt{- 192}$

Step 1

Rewrite $- 192$ as $- 1 (192)$ .

$\sqrt{- 1 (192)}$

Step 2

Rewrite $\sqrt{- 1 (192)}$ as $\sqrt{- 1} \cdot \sqrt{192}$ .

$\sqrt{- 1} \cdot \sqrt{192}$

Step 3

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

$i \cdot \sqrt{192}$

Step 4

Rewrite $192$ as $8^{2} \cdot 3$ .

Factor $64$ out of $192$ .

$i \cdot \sqrt{64 (3)}$

Rewrite $64$ as $8^{2}$ .

$i \cdot \sqrt{8^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

$i \cdot (8 \sqrt{3})$

Step 6

Move $8$ to the left of $i$ .

$8 i \sqrt{3}$