Answer
$\dfrac{31\sqrt3}{14}$
Work Step by Step
Factor each radicand so that one of the factors is a perfect square to obtain:
\begin{align*}
&=\frac{\sqrt{9(3)}}{2}+\frac{\sqrt{25(3)}}{7}
\end{align*}
Simplify each radical to obtain:
\begin{align*}
&=\frac{3\sqrt3}{2}+\frac{5\sqrt3}{7}
\end{align*}
Make the expressions similar using their LCD which is $14$ to obtain:
\begin{align*}
&=\frac{3\sqrt3 \cdot 7}{2\cdot 7} + \frac{5\sqrt3 \cdot 2}{7\cdot 2}\\\\
&=\frac{21\sqrt3}{14}+\frac{10\sqrt3}{14}\\\\
&=\frac{(21+10)\sqrt3}{14}\\\\
&=\frac{31\sqrt3}{14}
\end{align*}
