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: 62

Answer

$-36\sqrt{2}$

Work Step by Step

Using the properties of radicals, the given expression, $ 4\sqrt{18}-6\sqrt{50}-3\sqrt{72} ,$ simplifies to \begin{array}{l}\require{cancel} 4\sqrt{9\cdot2}-6\sqrt{25\cdot2}-3\sqrt{36\cdot2} \\\\= 4\sqrt{(3)^2\cdot2}-6\sqrt{(5)^2\cdot2}-3\sqrt{(6)^2\cdot2} \\\\= 4\cdot3\sqrt{2}-6\cdot5\sqrt{2}-3\cdot6\sqrt{2} \\\\= 12\sqrt{2}-30\sqrt{2}-18\sqrt{2} \\\\= -36\sqrt{2} .\end{array}
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