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

Published by Pearson

# Chapter 10 - Exponents and Radicals - 10.1 Radical Expressions and Functions - 10.1 Exercise Set - Page 634: 38

#### Answer

$7|c|$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of radicals and absolute value to simplify the given expression, $\sqrt{(-7c)^2} .$ $\bf{\text{Solution Details:}}$ Since $\sqrt{x^2}=|x|$ for any real value $x,$ the expression above simplifies to \begin{array}{l}\require{cancel} \sqrt{(-7c)^2} \\\\= |-7c| .\end{array} Since $|cx|=|c|\cdot|x|$ where $c$ is a constant, then \begin{array}{l}\require{cancel} |-7c| \\\\= |-7|\cdot|c| \\\\= 7|c| .\end{array}

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