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

$23+8\sqrt{7}$
Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, and the properties of radicals, the given expression, $(4+\sqrt{7})^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (4)^2+2(4)(\sqrt{7})+(\sqrt{7})^2 \\\\= 16+8\sqrt{7}+7 \\\\= 23+8\sqrt{7} .\end{array}