Answer
$\dfrac{15}{\sqrt{30}}$
Work Step by Step
Rationalizing the numerator, the given expression, $
\dfrac{3\sqrt{10}}{2\sqrt{3}}
,$ is equivalent to
\begin{array}{l}
\dfrac{3\sqrt{10}}{2\sqrt{3}}\cdot\dfrac{\sqrt{10}}{\sqrt{10}}
\\\\=
\dfrac{3\sqrt{10^2}}{2\sqrt{30}}
\\\\=
\dfrac{3(10)}{2\sqrt{30}}
\\\\=
\dfrac{30}{2\sqrt{30}}
\\\\=
\dfrac{15}{\sqrt{30}}
.\end{array}