Simplify square root of 9* square root of -9

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

$\sqrt{3^{2}} \cdot (i \cdot \sqrt{9})$

Step 5

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

$3 \cdot (i \cdot \sqrt{9})$

Step 6

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

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

Step 7

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

$3 \cdot (i \cdot 3)$

Step 8

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

$3 \cdot (3 \cdot i)$

Step 9

Multiply $3$ by $3$ .

$9 i$