Answer
$25+10\sqrt{6}$
Work Step by Step
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 given expression, $
(\sqrt{15}+\sqrt{10})^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{15})^2+2(\sqrt{15})(\sqrt{10})+(\sqrt{10})^2
\\\\=
15+2\left(\sqrt{15(10)}\right)+10
\\\\=
25+2\left(\sqrt{150}\right)
.\end{array}
Extracting the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
25+2\left(\sqrt{150}\right)
\\\\=
25+2\left(\sqrt{25\cdot6}\right)
\\\\=
25+2\left(\sqrt{(5)^2\cdot6}\right)
\\\\=
25+2(5)\left(\sqrt{6}\right)
\\\\=
25+10\sqrt{6}
.\end{array}
