Simplify ( square root of 10)(-3 square root of -7)

$(\sqrt{10}) (- 3 \sqrt{- 7})$

Rewrite $- 7$ as $- 1 (7)$ .

$\sqrt{10} (- 3 \sqrt{- 1 (7)})$

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$\sqrt{10} (- 3 (\sqrt{- 1} \cdot \sqrt{7}))$

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

$\sqrt{10} (- 3 (i \cdot \sqrt{7}))$

Multiply $\sqrt{10} (- 3 i \sqrt{7})$ .

Combine using the product rule for radicals.

$- 3 i \sqrt{10 \cdot 7}$

Multiply $10$ by $7$ .

$- 3 i \sqrt{70}$