Answer
$\dfrac{3\sqrt{3}}{2y}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{\dfrac{27}{4y^2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{9}{4y^2}\cdot3}
\\\\=
\sqrt{\left( \dfrac{3}{2y} \right)^2\cdot3}
\\\\=
\dfrac{3}{2y}\sqrt{3}
\\\\=
\dfrac{3\sqrt{3}}{2y}
.\end{array}
Note that all variables are assumed to represent positive real numbers.
