Simplify the Radical Expression (5 square root of -1)(-5 square root of 16)

$(5 \sqrt{- 1}) (- 5 \sqrt{16})$

Step 1

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

$5 i (- 5 \sqrt{16})$

Step 2

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

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

Step 3

Pull terms out from under the radical.

$5 i (- 5 | 4 |)$

Step 4

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

$5 i (- 5 \cdot 4)$

Step 5

Multiply $- 5$ by $4$ .

$5 i \cdot - 20$

Step 6

Multiply $- 20$ by $5$ .

$- 100 i$