Answer
$\dfrac{\sqrt{6xy}}{8x}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{\sqrt{3y}}{\sqrt{32x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{3y}}{\sqrt{16\cdot2x}}
\\\\=
\dfrac{\sqrt{3y}}{\sqrt{(4)^2\cdot2x}}
\\\\=
\dfrac{\sqrt{3y}}{4\sqrt{2x}}
\\\\=
\dfrac{\sqrt{3y}}{4\sqrt{2x}}\cdot\dfrac{\sqrt{2x}}{\sqrt{2x}}
\\\\=
\dfrac{\sqrt{6xy}}{4\cdot2x}
\\\\=
\dfrac{\sqrt{6xy}}{8x}
.\end{array}
Note that all variables are assumed to represent positive real numbers.
