Evaluate square root of -27

$\sqrt{- 27}$

Step 1

Rewrite $- 27$ as $- 1 (27)$ .

$\sqrt{- 1 (27)}$

Step 2

Rewrite $\sqrt{- 1 (27)}$ as $\sqrt{- 1} \cdot \sqrt{27}$ .

$\sqrt{- 1} \cdot \sqrt{27}$

Step 3

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

$i \cdot \sqrt{27}$

Step 4

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$i \cdot \sqrt{9 (3)}$

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

$i \cdot \sqrt{3^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

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

Step 6

Move $3$ to the left of $i$ .

$3 i \sqrt{3}$