Intermediate Algebra (12th Edition)

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

Chapter 7 - Summary Exercises - Performing Operations with Radicals and Rational Exponents: 18

Answer

$\dfrac{\sqrt{15x}}{5x}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To rationalize the given radical expression, $ \sqrt{\dfrac{3}{5x}} ,$ multiply the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index. Then use the laws of radicals to simplify the result $\bf{\text{Solution Details:}}$ Multiplying the radicand 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{\dfrac{3}{5x}\cdot\dfrac{5x}{5x}} \\\\= \sqrt{\dfrac{15x}{(5x)^2}} .\end{array} Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt{15x}}{\sqrt{(5x)^2}} \\\\= \dfrac{\sqrt{15x}}{5x} .\end{array}
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