Answer
$13+4\sqrt{10}$.
Work Step by Step
The given expression is
$=(\sqrt{5}+\sqrt{8})^2$
Use the special formula $(A+B)^2=A^2+2AB+B^2$
We have $A=\sqrt5$ and $B=\sqrt8$.
$=(\sqrt{5})^2+2(\sqrt{5})(\sqrt{8})+(\sqrt{8})^2$
Use product rule.
$=5+2\sqrt{5\cdot 8}+8$
Simplify.
$=13+2\sqrt{40}$
Factor the radicand as a perfect square.
$=13+2\sqrt{2^2\cdot 10}$
Simplify.
$=13+4\sqrt{10}$.
