Evaluate square root of -84

$\sqrt{- 84}$

Step 1

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

$\sqrt{- 1 (84)}$

Step 2

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

$\sqrt{- 1} \cdot \sqrt{84}$

Step 3

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

$i \cdot \sqrt{84}$

Step 4

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

Factor $4$ out of $84$ .

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

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

$i \cdot \sqrt{2^{2} \cdot 21}$

Step 5

Pull terms out from under the radical.

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

Step 6

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

$2 i \sqrt{21}$