# Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 58

$x+8\sqrt{x-3}+13$

#### Work Step by Step

Using $(a+b)^2=a^2+2ab+b^2$, or the square of a binomial, and the properties of radicals, the given expression, $(4+\sqrt{x-3})^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (4)^2+2(4)(\sqrt{x-3})+(\sqrt{x-3})^2 \\\\= 16+8\sqrt{x-3}+x-3 \\\\= x+8\sqrt{x-3}+(-3+16) \\\\= x+8\sqrt{x-3}+13 .\end{array}

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