Simplify ( square root of 6)(6 square root of -80)

$(\sqrt{6}) (6 \sqrt{- 80})$

Rewrite $- 80$ as $- 1 (80)$ .

$\sqrt{6} (6 \sqrt{- 1 (80)})$

Rewrite $\sqrt{- 1 (80)}$ as $\sqrt{- 1} \cdot \sqrt{80}$ .

$\sqrt{6} (6 (\sqrt{- 1} \cdot \sqrt{80}))$

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

$\sqrt{6} (6 (i \cdot \sqrt{80}))$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{6} (6 (i \cdot \sqrt{16 (5)}))$

Rewrite $16$ as $4^{2}$ .

$\sqrt{6} (6 (i \cdot \sqrt{4^{2} \cdot 5}))$

Pull terms out from under the radical.

$\sqrt{6} (6 (i \cdot (4 \sqrt{5})))$

Simplify the expression.

Move $4$ to the left of $i$ .

$\sqrt{6} (6 (4 \cdot i \sqrt{5}))$

Multiply $4$ by $6$ .

$\sqrt{6} (24 (i \sqrt{5}))$

Multiply $\sqrt{6} (24 i \sqrt{5})$ .

Combine using the product rule for radicals.

$24 i \sqrt{6 \cdot 5}$

Multiply $6$ by $5$ .

$24 i \sqrt{30}$