Find the Exact Value 3 square root of -27

$3 \sqrt{- 27}$

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

$3 \sqrt{- 1 (27)}$

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

$3 (\sqrt{- 1} \cdot \sqrt{27})$

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

$3 (i \cdot \sqrt{27})$

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

Factor $9$ out of $27$ .

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

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

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

Pull terms out from under the radical.

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

Simplify the expression.

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

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

Multiply $3$ by $3$ .

$9 i \sqrt{3}$