Answer
$-2 - 3i\sqrt{2}$
Work Step by Step
Factor the radicand so that one factor $-1$ to obtain:
$=-2-\sqrt{18(-1)}
\\=-2-\sqrt{2(9)(-1)}
\\=-2-\sqrt{2(3^2)(-1)}$
RECALL:
(1) $\sqrt{abc} = \sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}$
(2) $\sqrt{-1} = i$
Use rule (1) above to obtain:
$=-2 - \sqrt{2} \cdot \sqrt{3^2} \cdot \sqrt{-1}
\\=-2 - \sqrt{2} \cdot 3 \cdot \sqrt{-1}
\\= -2 - 3\sqrt{2} \cdot \sqrt{-1}$
Use rule (2) above to obtain:
$=-2 - 3\sqrt{2} \cdot i
\\=-2 - 3i\sqrt{2}$
