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: 57

Answer

$x-6\sqrt{x+5}+14$

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, $ (3-\sqrt{x+5})^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (3)^2+2(3)(-\sqrt{x+5})+(-\sqrt{x+5})^2 \\\\= 9-6\sqrt{x+5}+x+5 \\\\= x-6\sqrt{x+5}+(5+9) \\\\= x-6\sqrt{x+5}+14 .\end{array}
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