Answer
$-\dfrac{\sqrt{6}}{3}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{-3\sqrt{2}}{\sqrt{27}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{-3\sqrt{2}}{\sqrt{9\cdot3}}
\\\\=
\dfrac{-3\sqrt{2}}{\sqrt{(3)^2\cdot3}}
\\\\=
\dfrac{-3\sqrt{2}}{3\sqrt{3}}
\\\\=
\dfrac{-\cancel{3}\sqrt{2}}{\cancel{3}\sqrt{3}}
\\\\=
\dfrac{-\sqrt{2}}{\sqrt{3}}
\\\\=
\dfrac{-\sqrt{2}}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}
\\\\=
\dfrac{-\sqrt{6}}{3}
\\\\=
-\dfrac{\sqrt{6}}{3}
.\end{array}
