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 - 10.1 Radical Expressions and Functions - 10.1 Exercise Set: 41

Answer

$|y+8|$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Factor the radicand and use the properties of radicals to simplify the given expression, $ \sqrt{y^2+16y+64} .$ $\bf{\text{Solution Details:}}$ Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt{(y+8)^2} .\end{array} Since $\sqrt{x^2}=|x|$ for any real value $x,$ the expression above simplifies to \begin{array}{l}\require{cancel} \sqrt{(y+8)^2} \\\\= |y+8| .\end{array}
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