Simplify the Radical Expression (7 square root of 9)(7 square root of -16)

$(7 \sqrt{9}) (7 \sqrt{- 16})$

Step 1

Rewrite $- 16$ as $- 1 (16)$ .

$7 \sqrt{9} (7 \sqrt{- 1 (16)})$

Step 2

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$7 \sqrt{9} (7 (\sqrt{- 1} \cdot \sqrt{16}))$

Step 3

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

$7 \sqrt{9} (7 (i \cdot \sqrt{16}))$

Step 4

Rewrite $9$ as $3^{2}$ .

$7 \sqrt{3^{2}} (7 (i \cdot \sqrt{16}))$

Step 5

Pull terms out from under the radical.

$7 | 3 | (7 (i \cdot \sqrt{16}))$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$7 \cdot 3 (7 (i \cdot \sqrt{16}))$

Step 7

Multiply $7$ by $3$ .

$21 (7 (i \cdot \sqrt{16}))$

Step 8

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

$21 (7 (i \cdot \sqrt{4^{2}}))$

Step 9

Pull terms out from under the radical.

$21 (7 (i \cdot | 4 |))$

Step 10

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

$21 (7 (i \cdot 4))$

Step 11

Move $4$ to the left of $i$ .

$21 (7 (4 \cdot i))$

Step 12

Multiply $4$ by $7$ .

$21 (28 i)$

Step 13

Multiply $28$ by $21$ .

$588 i$