Answer
$\sqrt{6 5}+2\sqrt{13}$.
Work Step by Step
The given expression is
$=\frac{\sqrt{13}}{\sqrt{5}-2}$
The conjugate of $\sqrt{5}-2$ is $\sqrt{5}+2$.
Multiply by $\frac{\sqrt{5}+2}{\sqrt{5}+2}$.
$=\frac{\sqrt{13}}{\sqrt{5}-2}\cdot \frac{\sqrt{5}+2}{\sqrt{5}+2}$
Use sum and difference pattern.
$=\frac{\sqrt{13}(\sqrt{5}+2)}{(\sqrt{5})^2-2^2}$
Simplify.
$=\frac{\sqrt{13}(\sqrt{5}+2)}{5-4}$
$=\frac{\sqrt{13}(\sqrt{5}+2)}{1}$
Use distributive property.
$=\sqrt{13}\cdot \sqrt{5}+\sqrt{13}\cdot 2$
Use product property of square roots.
$=\sqrt{13\cdot 5}+2\sqrt{13}$
Simplify.
$=\sqrt{6 5}+2\sqrt{13}$.
