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 - Study Summary - Practice Exercises - Page 690: 8



Work Step by Step

Extracting the factor that is a perfet power of the index, then \begin{array}{l}\require{cancel} \sqrt{\dfrac{12x^3}{25}} \\\\= \sqrt{\dfrac{4x^2}{25}\cdot3x} \\\\= \sqrt{\left( \dfrac{2x}{5} \right)^2\cdot3x} .\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{\left( \dfrac{2x}{5} \right)^2\cdot3x} \\\\= \left| \dfrac{2x}{5} \right|\sqrt{3x} \\\\= \left| \dfrac{2}{5} \right|\cdot|x|\sqrt{3x} \\\\= \dfrac{2}{5}|x|\sqrt{3x} \\\\= \dfrac{2|x|\sqrt{3x}}{5} .\end{array}
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