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: 64

Answer

$-\dfrac{5\sqrt{3}}{6}$

Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{1}{3}\sqrt{12}-\dfrac{3}{2}\sqrt{48}+\dfrac{3}{4}\sqrt{108} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{3}\sqrt{4\cdot3}-\dfrac{3}{2}\sqrt{16\cdot3}+\dfrac{3}{4}\sqrt{36\cdot3} \\\\= \dfrac{1}{3}\sqrt{(2)^2\cdot3}-\dfrac{3}{2}\sqrt{(4)^2\cdot3}+\dfrac{3}{4}\sqrt{(6)^2\cdot3} \\\\= \dfrac{1}{3}\cdot2\sqrt{3}-\dfrac{3}{2}\cdot4\sqrt{3}+\dfrac{3}{4}\cdot6\sqrt{3} \\\\= \dfrac{2}{3}\sqrt{3}-\dfrac{3}{\cancel{2}}\cdot\cancel{2}(2)\sqrt{3}+\dfrac{3}{\cancel{2}(2)}\cdot\cancel{2}(3)\sqrt{3} \\\\= \dfrac{2}{3}\sqrt{3}-6\sqrt{3}+\dfrac{9}{2}\sqrt{3} \\\\= \dfrac{4}{6}\sqrt{3}-\dfrac{36}{6}\sqrt{3}+\dfrac{27}{6}\sqrt{3} \\\\= -\dfrac{5}{6}\sqrt{3} \\\\= -\dfrac{5\sqrt{3}}{6} .\end{array}
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