Answer
$3xy\sqrt{3x}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{3}{4}\sqrt{48x^3y^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3}{4}\sqrt{16x^2y^2\cdot3x}
\\\\=
\dfrac{3}{4}\sqrt{(4xy)^2\cdot3x}
\\\\=
\dfrac{3}{4}\cdot4xy\sqrt{3x}
\\\\=
\dfrac{3}{\cancel{4}}\cdot\cancel{4}xy\sqrt{3x}
\\\\=
3xy\sqrt{3x}
.\end{array}
