Simplify square root of -8

$\sqrt{- 8}$

Step 1

Rewrite $- 8$ as $- 1 (8)$ .

$\sqrt{- 1 (8)}$

Step 2

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$\sqrt{- 1} \cdot \sqrt{8}$

Step 3

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

$i \cdot \sqrt{8}$

Step 4

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

Factor $4$ out of $8$ .

$i \cdot \sqrt{4 (2)}$

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Move $2$ to the left of $i$ .

$2 i \sqrt{2}$