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: 45

Answer

$5\sqrt{3}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To rationalize the given radical expression, $ \dfrac{15}{\sqrt{3}} ,$ multiply both the numerator and the denominator by an expression that will make the denominator a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying both the numerator and the denominator by an expression that will make the denominator a perfect power of the index results to \begin{array}{l}\require{cancel} \dfrac{15}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}} \\\\= \dfrac{15\sqrt{3}}{\sqrt{3}\sqrt{3}} .\end{array} Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{15\sqrt{3}}{\sqrt{3(3)}} \\\\= \dfrac{15\sqrt{3}}{\sqrt{3^2}} \\\\= \dfrac{15\sqrt{3}}{3} \\\\= \dfrac{\cancel{3}(5)\sqrt{3}}{\cancel{3}} \\\\= 5\sqrt{3} .\end{array}
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