Answer
$15+10\sqrt{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(\sqrt{5}+\sqrt{10})^2
,$ use the special product on squaring binomials.
$\bf{\text{Solution Details:}}$
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{5})^2+2(\sqrt{5})(\sqrt{10})+(\sqrt{10})^2
\\\\=
5+2\sqrt{5(10)}+10
\\\\=
(5+10)+2\sqrt{50}
\\\\=
15+2\sqrt{25\cdot2}
\\\\=
15+2\sqrt{(5)^2\cdot2}
\\\\=
15+2(5)\sqrt{2}
\\\\=
15+10\sqrt{2}
.\end{array}
