Elementary Algebra

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

Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 38



Work Step by Step

Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $ \dfrac{6\sqrt{12}}{5\sqrt{24}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{6}{5}\sqrt{\dfrac{12}{24}} \\\\= \dfrac{6}{5}\sqrt{\dfrac{1}{2}} \\\\= \dfrac{6}{5}\sqrt{\dfrac{1}{2}\cdot\dfrac{2}{2}} \\\\= \dfrac{6}{5}\sqrt{\dfrac{2}{4}} \\\\= \dfrac{6}{5}\cdot\dfrac{\sqrt{2}}{\sqrt{4}} \\\\= \dfrac{6}{5}\cdot\dfrac{\sqrt{2}}{\sqrt{(2)^2}} \\\\= \dfrac{6}{5}\cdot\dfrac{\sqrt{2}}{2} \\\\= \dfrac{\cancel{2}(3)}{5}\cdot\dfrac{\sqrt{2}}{\cancel{2}} \\\\= \dfrac{3\sqrt{2}}{5} .\end{array}
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