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

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

Rewrite $- 10$ as $- 1 (10)$ .

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

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

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

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

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

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

Multiply $7$ by $- 10$ .

$- 70 \sqrt{3} (i \sqrt{10})$

Combine using the product rule for radicals.

$- 70 \sqrt{10 \cdot 3} i$

Multiply $10$ by $3$ .

$- 70 \sqrt{30} i$