Intermediate Algebra (12th Edition)

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

Chapter 7 - Section 7.4 - Adding and Subtracting Radical Expressions - 7.4 Exercises: 44

Answer

$4\sqrt{3}-3$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ \sqrt{48}-\dfrac{\sqrt{81}}{\sqrt{9}} ,$ simplify first each term by using the laws of radicals and by extracting the factor of the radicand that is a perfect power of the index. Then combine the like radicals. $\bf{\text{Solution Details:}}$ 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} \sqrt{48}-\sqrt{\dfrac{81}{9}} \\\\= \sqrt{48}-\sqrt{9} .\end{array} Rewriting the radicand as an expression that contains a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt{16\cdot3}-\sqrt{9} \\\\= \sqrt{(4)^2\cdot3}-\sqrt{(3)^2} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 4\sqrt{3}-3 .\end{array}
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