Simplify square root of -9

$\sqrt{- 9}$

Step 1

Rewrite $- 9$ as $- 1 (9)$ .

$\sqrt{- 1 (9)}$

Step 2

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$\sqrt{- 1} \cdot \sqrt{9}$

Step 3

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

$i \cdot \sqrt{9}$

Step 4

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

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

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 3$

Step 6

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

$3 i$