Evaluate square root of -288

$\sqrt{- 288}$

Step 1

Rewrite $- 288$ as $- 1 (288)$ .

$\sqrt{- 1 (288)}$

Step 2

Rewrite $\sqrt{- 1 (288)}$ as $\sqrt{- 1} \cdot \sqrt{288}$ .

$\sqrt{- 1} \cdot \sqrt{288}$

Step 3

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

$i \cdot \sqrt{288}$

Step 4

Rewrite $288$ as $12^{2} \cdot 2$ .

Factor $144$ out of $288$ .

$i \cdot \sqrt{144 (2)}$

Rewrite $144$ as $12^{2}$ .

$i \cdot \sqrt{12^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$i \cdot (12 \sqrt{2})$

Step 6

Move $12$ to the left of $i$ .

$12 i \sqrt{2}$