Answer
$\dfrac{\sqrt{15xy}}{9y}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{\sqrt{5x}}{\sqrt{27y}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{5x}}{\sqrt{9\cdot3y}}
\\\\=
\dfrac{\sqrt{5x}}{\sqrt{(3)^2\cdot3y}}
\\\\=
\dfrac{\sqrt{5x}}{3\sqrt{3y}}
\\\\=
\dfrac{\sqrt{5x}}{3\sqrt{3y}}\cdot\dfrac{\sqrt{3y}}{\sqrt{3y}}
\\\\=
\dfrac{\sqrt{15xy}}{3\cdot3y}
\\\\=
\dfrac{\sqrt{15xy}}{9y}
.\end{array}
Note that all variables are assumed to represent positive real numbers.