Answer
$ \frac{43\sqrt {2}}{35} $.
Work Step by Step
The given expression is
$=\frac{\sqrt {32}}{5}+\frac{\sqrt {18}}{7}$
Factor the radicands into square terms.
$=\frac{\sqrt {4^2\cdot 2}}{5}+\frac{\sqrt {3^2\cdot 2}}{7}$
Simplify.
$=\frac{4\sqrt {2}}{5}+\frac{3\sqrt { 2}}{7}$
Using the distributive property:
$=\sqrt {2} \left ( \frac{4}{5}+\frac{3}{7} \right )$
Multiply and divide the first fraction by $7$ and the second by $5$
$=\sqrt {2} \left ( \frac{7\cdot 4}{7\cdot 5}+\frac{5\cdot 3}{5\cdot 7} \right )$
$=\sqrt {2} \left ( \frac{28}{35}+\frac{15}{35} \right )$
$=\sqrt {2} \left ( \frac{28+15}{35} \right )$
Simplify.
$=\sqrt {2} \left ( \frac{43}{35} \right )$
Clear the parentheses.
$= \frac{43\sqrt {2}}{35} $.
