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

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

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

Answer

$23+8\sqrt{7}$

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{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}
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