Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 51

$23+8\sqrt{7}$

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}