Simplify (-6 square root of 6)(10 square root of -30)

$(- 6 \sqrt{6}) (10 \sqrt{- 30})$

Step 1

Rewrite $- 30$ as $- 1 (30)$ .

$- 6 \sqrt{6} (10 \sqrt{- 1 (30)})$

Step 2

Rewrite $\sqrt{- 1 (30)}$ as $\sqrt{- 1} \cdot \sqrt{30}$ .

$- 6 \sqrt{6} (10 (\sqrt{- 1} \cdot \sqrt{30}))$

Step 3

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

$- 6 \sqrt{6} (10 (i \cdot \sqrt{30}))$

Step 4

Multiply $- 6 \sqrt{6} (10 i \sqrt{30})$ .

Multiply $10$ by $- 6$ .

$- 60 \sqrt{6} (i \sqrt{30})$

Combine using the product rule for radicals.

$- 60 \sqrt{30 \cdot 6} i$

Multiply $30$ by $6$ .

$- 60 \sqrt{180} i$

Step 5

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$- 60 \sqrt{36 (5)} i$

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

$- 60 \sqrt{6^{2} \cdot 5} i$

Step 6

Pull terms out from under the radical.

$- 60 (6 \sqrt{5}) i$

Step 7

Multiply $6$ by $- 60$ .

$- 360 \sqrt{5} i$