Answer
$-6i\sqrt{3}$
Work Step by Step
Factor the radicand so that one factor $-1$ to obtain:
$=-\sqrt{108(-1)}
\\=-\sqrt{36(3)(-1)}
\\=-\sqrt{6^2(3)(-1)}$
RECALL:
(1) $\sqrt{abc} = \sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}$
(2) $\sqrt{-1} = i$
Use rule (1) above to obtain:
$=-\sqrt{6^2} \cdot \sqrt{3} \cdot \sqrt{-1}
\\=-6 \cdot \sqrt{3} \cdot \sqrt{-1}
\\=-6\sqrt{3} \cdot \sqrt{-1}$
Use rule (2) above to obtain:
$=-6\sqrt{3} \cdot i
\\=-6i\sqrt{3}$
