Simplify square root of -108

$\sqrt{- 108}$

Rewrite $- 108$ as $- 1 (108)$ .

$\sqrt{- 1 (108)}$

Rewrite $\sqrt{- 1 (108)}$ as $\sqrt{- 1} \cdot \sqrt{108}$ .

$\sqrt{- 1} \cdot \sqrt{108}$

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

$i \cdot \sqrt{108}$

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$i \cdot \sqrt{36 (3)}$

Rewrite $36$ as $6^{2}$ .

$i \cdot \sqrt{6^{2} \cdot 3}$

Pull terms out from under the radical.

$i \cdot (6 \sqrt{3})$

Move $6$ to the left of $i$ .

$6 i \sqrt{3}$