Simplify (2 square root of -49)(- square root of 36)

$(2 \sqrt{- 49}) (- \sqrt{36})$

Step 1

Rewrite $- 49$ as $- 1 (49)$ .

$2 \sqrt{- 1 (49)} (- \sqrt{36})$

Step 2

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$2 (\sqrt{- 1} \cdot \sqrt{49}) (- \sqrt{36})$

Step 3

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

$2 (i \cdot \sqrt{49}) (- \sqrt{36})$

Step 4

Rewrite $49$ as $7^{2}$ .

$2 (i \cdot \sqrt{7^{2}}) (- \sqrt{36})$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

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

Step 6

Move $7$ to the left of $i$ .

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

Step 7

Multiply $7$ by $2$ .

$14 i (- \sqrt{36})$

Step 8

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

$14 i (- \sqrt{6^{2}})$

Step 9

Multiply.

Pull terms out from under the radical, assuming positive real numbers.

$14 i (- 1 \cdot 6)$

Multiply $- 1$ by $6$ .

$14 i \cdot - 6$

Multiply $- 6$ by $14$ .

$- 84 i$