Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.2 - Simplifying Radicals - Problem Set 9.2: 65



Work Step by Step

Using the properties of radicals, the given expression, $ 3\sqrt{8}-5\sqrt{20}-7\sqrt{18}-9\sqrt{125} ,$ simplifies to \begin{array}{l}\require{cancel} 3\sqrt{4\cdot2}-5\sqrt{4\cdot5}-7\sqrt{9\cdot2}-9\sqrt{25\cdot5} \\\\= 3\sqrt{(2)^2\cdot2}-5\sqrt{(2)^2\cdot5}-7\sqrt{(3)^2\cdot2}-9\sqrt{(5)^2\cdot5} \\\\= 3\cdot2\sqrt{2}-5\cdot2\sqrt{5}-7\cdot3\sqrt{2}-9\cdot5\sqrt{5} \\\\= 6\sqrt{2}-10\sqrt{5}-21\sqrt{2}-45\sqrt{5} \\\\= (6\sqrt{2}-21\sqrt{2})+(-10\sqrt{5}-45\sqrt{5}) \\\\= -15\sqrt{2}-55\sqrt{5} .\end{array}
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