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: 63

Answer

$2\sqrt{5}$

Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{1}{2}\sqrt{20}+\dfrac{2}{3}\sqrt{45}-\dfrac{1}{4}\sqrt{80} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{2}\sqrt{4\cdot5}+\dfrac{2}{3}\sqrt{9\cdot5}-\dfrac{1}{4}\sqrt{16\cdot5} \\\\= \dfrac{1}{2}\sqrt{(2)^2\cdot5}+\dfrac{2}{3}\sqrt{(3)^2\cdot5}-\dfrac{1}{4}\sqrt{(4)^2\cdot5} \\\\= \dfrac{1}{2}\cdot2\sqrt{5}+\dfrac{2}{3}\cdot3\sqrt{5}-\dfrac{1}{4}\cdot4\sqrt{5} \\\\= \sqrt{5}+2\sqrt{5}-\sqrt{5} \\\\= 2\sqrt{5} .\end{array}
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