Simplify ( square root of 9)(8 square root of -28)

$(\sqrt{9}) (8 \sqrt{- 28})$

Rewrite $- 28$ as $- 1 (28)$ .

$\sqrt{9} (8 \sqrt{- 1 (28)})$

Rewrite $\sqrt{- 1 (28)}$ as $\sqrt{- 1} \cdot \sqrt{28}$ .

$\sqrt{9} (8 (\sqrt{- 1} \cdot \sqrt{28}))$

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

$\sqrt{9} (8 (i \cdot \sqrt{28}))$

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

$\sqrt{3^{2}} (8 (i \cdot \sqrt{28}))$

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

$3 (8 (i \cdot \sqrt{28}))$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$3 (8 (i \cdot \sqrt{4 (7)}))$

Rewrite $4$ as $2^{2}$ .

$3 (8 (i \cdot \sqrt{2^{2} \cdot 7}))$

Pull terms out from under the radical.

$3 (8 (i \cdot (2 \sqrt{7})))$

Simplify the expression.

Move $2$ to the left of $i$ .

$3 (8 (2 \cdot i \sqrt{7}))$

Multiply $2$ by $8$ .

$3 (16 (i \sqrt{7}))$

Multiply $16$ by $3$ .

$48 i \sqrt{7}$