Simplify the Radical Expression (4 square root of 6)( square root of -5)

$(4 \sqrt{6}) (\sqrt{- 5})$

Rewrite $- 5$ as $- 1 (5)$ .

$4 \sqrt{6} \sqrt{- 1 (5)}$

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$4 \sqrt{6} (\sqrt{- 1} \cdot \sqrt{5})$

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

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

Multiply $4 \sqrt{6} (i \sqrt{5})$ .

Combine using the product rule for radicals.

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

Multiply $5$ by $6$ .

$4 \sqrt{30} i$