Answer
$\color{blue}{15+10\sqrt2}$
Work Step by Step
RECALL:
$(a+b)^2=a^2+2ab+b^2$
Use the formula above with $a=\sqrt5$ and $b=\sqrt{10}$ to obtain:
$(\sqrt5+\sqrt{10})^2
\\=(\sqrt5)^2+2(\sqrt5)(\sqrt{10}) + (\sqrt{10})^2
\\=5 + 2\sqrt{5\cdot10}+10
\\=15 + 2\sqrt{50}$
Factor the radicand so that one factor is a perfect square, then bring out the square root of the perfect square factor to obtain:
$=15+2\sqrt{25(2)}
\\=15+2(5)\sqrt2
\\=\color{blue}{15+10\sqrt2}$
