Answer
$9+2\sqrt{14}$
Work Step by Step
RECALL:
$(a+b)^2=a^2+2ab+b^2$
Use the formula above with $a=\sqrt{2}$ and $b=\sqrt{7}$ to obtain:
$=(\sqrt{2})^2 + 2\sqrt{2} \cdot \sqrt{7} + (\sqrt{7})^2$
Use the rules $(\sqrt{a})^2=a, a \ge 0$ and $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}, a, b, \ge 0$ to obtain:
$\\=2 + 2\sqrt{2(7)} + 7
\\=9+2\sqrt{14}$
