Answer
$\frac{7\sqrt{10}+2\sqrt{ 5}}{47}$
Work Step by Step
The given expression is
$=\frac{\sqrt{10}}{7-\sqrt{2}}$
The conjugate of $7-\sqrt{2}$ is $7+\sqrt{2}$
$=\frac{\sqrt{10}}{7-\sqrt{2}} \cdot \frac{7+\sqrt{2}}{7+\sqrt{2}}$
Use sum and difference pattern.
$=\frac{\sqrt{10}(7+\sqrt{2})}{7^2-(\sqrt{2})^2}$
Simplify.
$=\frac{7\sqrt{10}+\sqrt{10\cdot 2}}{49-2}$
$=\frac{7\sqrt{10}+\sqrt{4\cdot 5}}{47}$
$=\frac{7\sqrt{10}+2\sqrt{ 5}}{47}$
