Answer
$ \frac{31\sqrt {3}}{14} $.
Work Step by Step
The given expression is
$=\frac{\sqrt {27}}{2}+\frac{\sqrt {75}}{7}$
Factor the radicands into square terms.
$=\frac{\sqrt {3^2\cdot 3}}{2}+\frac{\sqrt {5^2\cdot 3}}{7}$
Simplify.
$=\frac{3\sqrt {3}}{2}+\frac{5\sqrt { 3}}{7}$
By using the distributive property:
$=\sqrt {3} \left ( \frac{3}{2}+\frac{5}{7} \right )$
Multiply and divide the first fraction by $7$ and the second by $2$
$=\sqrt {3} \left ( \frac{7\cdot 3}{7\cdot 2}+\frac{2\cdot 5}{2\cdot 7} \right )$
$=\sqrt {3} \left ( \frac{21}{14}+\frac{10}{14} \right )$
$=\sqrt {3} \left ( \frac{21+10}{14} \right )$
Simplify.
$=\sqrt {3} \left ( \frac{31}{14} \right )$
Clear the parentheses.
$= \frac{31\sqrt {3}}{14} $.
