Simplify (6 square root of 9)( square root of -6)

$(6 \sqrt{9}) (\sqrt{- 6})$

Step 1

Rewrite $- 6$ as $- 1 (6)$ .

$6 \sqrt{9} \sqrt{- 1 (6)}$

Step 2

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$6 \sqrt{9} (\sqrt{- 1} \cdot \sqrt{6})$

Step 3

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

$6 \sqrt{9} (i \cdot \sqrt{6})$

Step 4

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

$6 \sqrt{3^{2}} (i \cdot \sqrt{6})$

Step 5

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

$6 \cdot 3 (i \cdot \sqrt{6})$

Step 6

Multiply $6$ by $3$ .

$18 i \sqrt{6}$