Answer
$6-3i\sqrt{2}$
Work Step by Step
Using the properties of radicals and that $i=\sqrt{-1}$, then the given expression, $
6-\sqrt{-18}
,$ is equivalent to
\begin{array}{l}\require{cancel}
6-\sqrt{-1}\cdot\sqrt{18}
\\\\=
6-i\cdot\sqrt{9\cdot2}
\\\\=
6-i\cdot\sqrt{(3)^2\cdot2}
\\\\=
6-i\cdot3\sqrt{2}
\\\\=
6-3i\sqrt{2}
.\end{array}