Simplify the Radical Expression (6 square root of 16)( square root of -49)

$(6 \sqrt{16}) (\sqrt{- 49})$

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

$6 \sqrt{16} \sqrt{- 1 (49)}$

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

$6 \sqrt{16} (\sqrt{- 1} \cdot \sqrt{49})$

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

$6 \sqrt{16} (i \cdot \sqrt{49})$

Rewrite $16$ as $4^{2}$ .

$6 \sqrt{4^{2}} (i \cdot \sqrt{49})$

Pull terms out from under the radical.

$6 | 4 | (i \cdot \sqrt{49})$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$6 \cdot 4 (i \cdot \sqrt{49})$

Multiply $6$ by $4$ .

$24 (i \cdot \sqrt{49})$

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

$24 (i \cdot \sqrt{7^{2}})$

Pull terms out from under the radical.

$24 (i \cdot | 7 |)$

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$24 (i \cdot 7)$

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

$24 (7 \cdot i)$

Multiply $7$ by $24$ .

$168 i$