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 - Review Exercises: Chapter 10: 15

Answer

$|2x+1|$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of radicals to simplify the given expression, $ \sqrt{4x^2+4x+1} .$ $\bf{\text{Solution Details:}}$ 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{4x^2+4x+1} \\\\= \sqrt{(2x+1)^2} .\end{array} Using $\sqrt[n]{x^n}=|x|$ if $n$ is even and $\sqrt[n]{x^n}=x$ if $n$ is odd, then \begin{array}{l}\require{cancel} \sqrt{(2x+1)^2} \\\\= |2x+1| .\end{array}
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