Simplify - square root of 144* square root of -9

$- \sqrt{144} \cdot \sqrt{- 9}$

Step 1

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

$- \sqrt{144} \cdot \sqrt{- 1 (9)}$

Step 2

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

$- \sqrt{144} \cdot (\sqrt{- 1} \cdot \sqrt{9})$

Step 3

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

$- \sqrt{144} \cdot (i \cdot \sqrt{9})$

Step 4

Rewrite $144$ as $12^{2}$ .

$- \sqrt{12^{2}} \cdot (i \cdot \sqrt{9})$

Step 5

Multiply.

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

$- 1 \cdot 12 \cdot (i \cdot \sqrt{9})$

Multiply $- 1$ by $12$ .

$- 12 \cdot (i \cdot \sqrt{9})$

Step 6

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

$- 12 \cdot (i \cdot \sqrt{3^{2}})$

Step 7

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

$- 12 \cdot (i \cdot 3)$

Step 8

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

$- 12 \cdot (3 \cdot i)$

Step 9

Multiply $3$ by $- 12$ .

$- 36 i$