Answer
$-3 - 3i\sqrt{3}$
Work Step by Step
Factor the radicand so that one factor $-1$ to obtain:
$=-3-\sqrt{27(-1)}
\\=-3-\sqrt{3(9)(-1)}
\\=-3-\sqrt{3(3^2)(-1)}$
RECALL:
(1) $\sqrt{abc} = \sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}$
(2) $\sqrt{-1} = i$
Use rule (1) above to obtain:
$=-3 - \sqrt{3} \cdot \sqrt{3^2} \cdot \sqrt{-1}
\\=-3 - \sqrt{3} \cdot 3 \cdot \sqrt{-1}
\\= -3 - 3\sqrt{3} \cdot \sqrt{-1}$
Use rule (2) above to obtain:
$=-3- 3\sqrt{3} \cdot i
\\=-3 - 3i\sqrt{3}$
