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: 9

Answer

$20\sqrt{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ 5(\sqrt{72}-\sqrt{8}) ,$ simplify first each radical by extracting the root of the factor that is a perfect power of the index. Then combine like terms and multiply by $5$. $\bf{\text{Solution Details:}}$ Expressing the radicand with a factor that is a perfect power of the index, the given expression is equivalent to \begin{array}{l}\require{cancel} 5(\sqrt{36\cdot2}-\sqrt{4\cdot2}) \\\\= 5(\sqrt{(6)^2\cdot2}-\sqrt{(2)^2\cdot2}) .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 5(6\sqrt{2}-2\sqrt{2}) .\end{array} Combining the like radicals results to \begin{array}{l}\require{cancel} 5[(6-2)\sqrt{2}] \\\\= 5[4\sqrt{2}] \\\\= 20\sqrt{2} .\end{array}
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