Evaluate square root of -88

$\sqrt{- 88}$

Step 1

Rewrite $- 88$ as $- 1 (88)$ .

$\sqrt{- 1 (88)}$

Step 2

Rewrite $\sqrt{- 1 (88)}$ as $\sqrt{- 1} \cdot \sqrt{88}$ .

$\sqrt{- 1} \cdot \sqrt{88}$

Step 3

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

$i \cdot \sqrt{88}$

Step 4

Rewrite $88$ as $2^{2} \cdot 22$ .

Factor $4$ out of $88$ .

$i \cdot \sqrt{4 (22)}$

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

$i \cdot \sqrt{2^{2} \cdot 22}$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{22})$

Step 6

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

$2 i \sqrt{22}$