Evaluate 8 square root of -84

$8 \sqrt{- 84}$

Step 1

Rewrite $- 84$ as $- 1 (84)$ .

$8 \sqrt{- 1 (84)}$

Step 2

Rewrite $\sqrt{- 1 (84)}$ as $\sqrt{- 1} \cdot \sqrt{84}$ .

$8 (\sqrt{- 1} \cdot \sqrt{84})$

Step 3

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

$8 (i \cdot \sqrt{84})$

Step 4

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$8 (i \cdot \sqrt{4 (21)})$

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

$8 (i \cdot \sqrt{2^{2} \cdot 21})$

Step 5

Pull terms out from under the radical.

$8 (i \cdot (2 \sqrt{21}))$

Step 6

Simplify the expression.

Move $2$ to the left of $i$ .

$8 (2 \cdot i \sqrt{21})$

Multiply $2$ by $8$ .

$16 i \sqrt{21}$