Simplify (-5 square root of -3)( square root of 8)

$(- 5 \sqrt{- 3}) (\sqrt{8})$

Step 1

Rewrite $- 3$ as $- 1 (3)$ .

$- 5 \sqrt{- 1 (3)} \sqrt{8}$

Step 2

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$- 5 (\sqrt{- 1} \cdot \sqrt{3}) \sqrt{8}$

Step 3

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

$- 5 (i \cdot \sqrt{3}) \sqrt{8}$

Step 4

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$- 5 i \sqrt{3} \sqrt{4 (2)}$

Rewrite $4$ as $2^{2}$ .

$- 5 i \sqrt{3} \sqrt{2^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$- 5 i \sqrt{3} (2 \sqrt{2})$

Step 6

Multiply $- 5 i \sqrt{3} (2 \sqrt{2})$ .

Multiply $2$ by $- 5$ .

$- 10 i \sqrt{3} \sqrt{2}$

Combine using the product rule for radicals.

$- 10 i \sqrt{2 \cdot 3}$

Multiply $2$ by $3$ .

$- 10 i \sqrt{6}$