Elementary Algebra

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

Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set: 20

Answer

$\dfrac{2\sqrt{2}}{3}$

Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{4\sqrt{6}}{3\sqrt{12}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{4}{3}\sqrt{\dfrac{6}{12}} \\\\= \dfrac{4}{3}\sqrt{\dfrac{\cancel{6}}{\cancel{6}(2)}} \\\\= \dfrac{4}{3}\sqrt{\dfrac{1}{2}} \\\\= \dfrac{4}{3}\sqrt{\dfrac{1}{2}\cdot\dfrac{2}{2}} \\\\= \dfrac{4}{3}\sqrt{\dfrac{2}{4}} \\\\= \dfrac{4}{3}\cdot\dfrac{\sqrt{2}}{\sqrt{4}} \\\\= \dfrac{4}{3}\cdot\dfrac{\sqrt{2}}{2} \\\\= \dfrac{2\cdot \cancel{2}}{3}\cdot\dfrac{\sqrt{2}}{\cancel{2}} \\\\= \dfrac{2\sqrt{2}}{3} .\end{array}
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