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: 37

Answer

$\dfrac{\sqrt{21}}{8}$

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{3\sqrt{7}}{4\sqrt{12}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3\sqrt{7}}{4\sqrt{12}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}} \\\\= \dfrac{3\sqrt{21}}{4\sqrt{36}} \\\\= \dfrac{3\sqrt{21}}{4\sqrt{(6)^2}} \\\\= \dfrac{3\sqrt{21}}{4\cdot6} \\\\= \dfrac{\cancel{3}\sqrt{21}}{4\cdot\cancel{3}(2)} \\\\= \dfrac{\sqrt{21}}{8} .\end{array}
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