Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$19+6\sqrt{10}$
Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, and the properties of radicals, the given expression, $(3+\sqrt{10})^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (3)^2+2(3)(\sqrt{10})+(\sqrt{10})^2 \\\\= 9+6\sqrt{10}+10 \\\\= 19+6\sqrt{10} .\end{array}