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