# Chapter 10 - Exponents and Radicals - Review Exercises: Chapter 10 - Page 693: 15

$|2x+1|$

#### 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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