Simplify ( square root of -15)(-7 square root of 5)

$(\sqrt{- 15}) (- 7 \sqrt{5})$

Rewrite $- 15$ as $- 1 (15)$ .

$\sqrt{- 1 (15)} (- 7 \sqrt{5})$

Rewrite $\sqrt{- 1 (15)}$ as $\sqrt{- 1} \cdot \sqrt{15}$ .

$\sqrt{- 1} \cdot \sqrt{15} (- 7 \sqrt{5})$

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

$i \cdot \sqrt{15} (- 7 \sqrt{5})$

Multiply $i \sqrt{15} (- 7 \sqrt{5})$ .

Combine using the product rule for radicals.

$i (- 7 \sqrt{15 \cdot 5})$

Multiply $15$ by $5$ .

$i (- 7 \sqrt{75})$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$i (- 7 \sqrt{25 (3)})$

Rewrite $25$ as $5^{2}$ .

$i (- 7 \sqrt{5^{2} \cdot 3})$

Pull terms out from under the radical.

$i (- 7 (5 \sqrt{3}))$

Simplify the expression.

Multiply $5$ by $- 7$ .

$i (- 35 \sqrt{3})$

Reorder factors in $i (- 35 \sqrt{3})$ .

$- 35 i \sqrt{3}$