Answer
$\dfrac{2}{3}\sqrt{6xy}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{2}{9}\sqrt{54xy}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2}{9}\sqrt{9\cdot6xy}
\\\\=
\dfrac{2}{9}\sqrt{(3)^2\cdot6xy}
\\\\=
\dfrac{2}{9}\cdot3\sqrt{6xy}
\\\\=
\dfrac{2}{\cancel{3}\cdot3}\cdot\cancel{3}\sqrt{6xy}
\\\\=
\dfrac{2}{3}\sqrt{6xy}
.\end{array}
Note that all of the variables are assumed to represent non-negative real numbers.
