Answer
$8+2\sqrt{15}$
Work Step by Step
RECALL:
$(a+b)^2=a^2+2ab+b^2$
Use the formula above with $a=\sqrt{3}$ and $b=\sqrt{5}$ to obtain:
$=(\sqrt{3})^2 + 2\sqrt{3} \cdot \sqrt{5} + (\sqrt{5})^2$
Use the rules $(\sqrt{a})^2=a, a \ge 0$ and $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}, a, b, \ge 0$ to obtain:
$\\=3 + 2\sqrt{3(5)} + 5
\\=8+2\sqrt{15}$
