Simplify (- square root of 6)(-2 square root of -42)

$(- \sqrt{6}) (- 2 \sqrt{- 42})$

Step 1

Rewrite $- 42$ as $- 1 (42)$ .

$- \sqrt{6} (- 2 \sqrt{- 1 (42)})$

Step 2

Rewrite $\sqrt{- 1 (42)}$ as $\sqrt{- 1} \cdot \sqrt{42}$ .

$- \sqrt{6} (- 2 (\sqrt{- 1} \cdot \sqrt{42}))$

Step 3

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

$- \sqrt{6} (- 2 (i \cdot \sqrt{42}))$

Step 4

Multiply $- \sqrt{6} (- 2 i \sqrt{42})$ .

Multiply $- 2$ by $- 1$ .

$2 \sqrt{6} (i \sqrt{42})$

Combine using the product rule for radicals.

$2 \sqrt{42 \cdot 6} i$

Multiply $42$ by $6$ .

$2 \sqrt{252} i$

Step 5

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

Factor $36$ out of $252$ .

$2 \sqrt{36 (7)} i$

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

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

Step 6

Pull terms out from under the radical.

$2 (6 \sqrt{7}) i$

Step 7

Multiply $6$ by $2$ .

$12 \sqrt{7} i$