Simplify (3 square root of 10)(5 square root of -7)

$(3 \sqrt{10}) (5 \sqrt{- 7})$

Step 1

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

$3 \sqrt{10} (5 \sqrt{- 1 (7)})$

Step 2

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

$3 \sqrt{10} (5 (\sqrt{- 1} \cdot \sqrt{7}))$

Step 3

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

$3 \sqrt{10} (5 (i \cdot \sqrt{7}))$

Step 4

Multiply $3 \sqrt{10} (5 i \sqrt{7})$ .

Multiply $5$ by $3$ .

$15 \sqrt{10} (i \sqrt{7})$

Combine using the product rule for radicals.

$15 \sqrt{7 \cdot 10} i$

Multiply $7$ by $10$ .

$15 \sqrt{70} i$