Answer
$10+2\sqrt{21}$
Work Step by Step
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the given expression, $
\left( \sqrt{7}+\sqrt{3} \right)^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
(\sqrt{7})^2+2(\sqrt{7})(\sqrt{3})+(\sqrt{3})^2
\\\\=
7+2\sqrt{7(3)}+3
\\\\=
10+2\sqrt{21}
.\end{array}