Simplify square root of -99

$\sqrt{- 99}$

Step 1

Rewrite $- 99$ as $- 1 (99)$ .

$\sqrt{- 1 (99)}$

Step 2

Rewrite $\sqrt{- 1 (99)}$ as $\sqrt{- 1} \cdot \sqrt{99}$ .

$\sqrt{- 1} \cdot \sqrt{99}$

Step 3

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

$i \cdot \sqrt{99}$

Step 4

Rewrite $99$ as $3^{2} \cdot 11$ .

Factor $9$ out of $99$ .

$i \cdot \sqrt{9 (11)}$

Rewrite $9$ as $3^{2}$ .

$i \cdot \sqrt{3^{2} \cdot 11}$

Step 5

Pull terms out from under the radical.

$i \cdot (3 \sqrt{11})$

Step 6

Move $3$ to the left of $i$ .

$3 i \sqrt{11}$