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 - Page 407: 61



Work Step by Step

Using the properties of radicals, the given expression, $ 5\sqrt{12}+3\sqrt{27}-2\sqrt{75} ,$ simplifies to \begin{array}{l}\require{cancel} 5\sqrt{4\cdot3}+3\sqrt{9\cdot3}-2\sqrt{25\cdot3} \\\\= 5\sqrt{(2)^2\cdot3}+3\sqrt{(3)^2\cdot3}-2\sqrt{(5)^2\cdot3} \\\\= 5\cdot2\sqrt{3}+3\cdot3\sqrt{3}-2\cdot5\sqrt{3} \\\\= 10\sqrt{3}+9\sqrt{3}-10\sqrt{3} \\\\= 9\sqrt{3} .\end{array}
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