Answer
$\dfrac{43\sqrt2}{35}$
Work Step by Step
Factor each radicand so that one of the factors is a perfect square to obtain:
\begin{align*}
&=\frac{\sqrt{16(2)}}{5}+\frac{\sqrt{9(2)}}{7}
\end{align*}
Simplify each radical to obtain:
\begin{align*}
&=\frac{4\sqrt2}{5}+\frac{3\sqrt2}{7}
\end{align*}
Make the expressions similar using their LCD which is $35$ to obtain:
\begin{align*}
&=\frac{4\sqrt2 \cdot 7}{5\cdot 7} + \frac{3\sqrt2 \cdot 5}{7\cdot 5}\\\\
&=\frac{28\sqrt2}{35}+\frac{15\sqrt2}{35}\\\\
&=\frac{(28+15)\sqrt2}{35}\\\\
&=\frac{43\sqrt2}{35}
\end{align*}
