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