Simplify (10 square root of -6)( square root of 42)

$(10 \sqrt{- 6}) (\sqrt{42})$

Step 1

Rewrite $- 6$ as $- 1 (6)$ .

$10 \sqrt{- 1 (6)} \sqrt{42}$

Step 2

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$10 (\sqrt{- 1} \cdot \sqrt{6}) \sqrt{42}$

Step 3

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

$10 (i \cdot \sqrt{6}) \sqrt{42}$

Step 4

Multiply $10 i \sqrt{6} \sqrt{42}$ .

Combine using the product rule for radicals.

$10 i \sqrt{42 \cdot 6}$

Multiply $42$ by $6$ .

$10 i \sqrt{252}$

Step 5

Rewrite $252$ as $6^{2} \cdot 7$ .

Factor $36$ out of $252$ .

$10 i \sqrt{36 (7)}$

Rewrite $36$ as $6^{2}$ .

$10 i \sqrt{6^{2} \cdot 7}$

Step 6

Pull terms out from under the radical.

$10 i (6 \sqrt{7})$

Step 7

Multiply $6$ by $10$ .

$60 i \sqrt{7}$