Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.5 - Multiplying and Dividing Radical Expressions - 7.5 Exercises: 82

Answer

$\dfrac{\sqrt[4]{ 7ts^2}}{s}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To rationalize the given radical expression, $ \sqrt[4]{\dfrac{7t}{s^2}} ,$ multiply the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying the numerator and the denominator by an expression equal to $1$ which will make the denominator a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[4]{\dfrac{7t}{s^2}\cdot\dfrac{s^2}{s^2}} \\\\= \sqrt[4]{\dfrac{7ts^2}{s^4}} .\end{array} Rewriting the radicand using an expression that contains a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[4]{\dfrac{1}{s^4}\cdot 7ts^2} \\\\= \sqrt[4]{\left( \dfrac{1}{s} \right)^4\cdot 7ts^2} .\end{array} Extracting the root of the radicand that is a perfect power of the index results to \begin{array}{l}\require{cancel} \dfrac{1}{s}\sqrt[4]{ 7ts^2} \\\\= \dfrac{\sqrt[4]{ 7ts^2}}{s} .\end{array}
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