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: 55

Answer

$\dfrac{52\sqrt{5}}{5}$

Work Step by Step

Using the properties of radicals, the given expression, $ 4\sqrt{20}-\dfrac{3}{\sqrt{5}}+\sqrt{45} ,$ simplifies to \begin{array}{l}\require{cancel} 4\sqrt{4\cdot5}-\dfrac{3}{\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}+\sqrt{9\cdot5} \\\\= 4\sqrt{(2)^2\cdot5}-\dfrac{3\sqrt{5}}{5}+\sqrt{(3)^2\cdot5} \\\\= 4(2)\sqrt{5}-\dfrac{3\sqrt{5}}{5}+3\sqrt{5} \\\\= 8\sqrt{5}-\dfrac{3\sqrt{5}}{5}+3\sqrt{5} \\\\= \dfrac{40\sqrt{5}}{5}-\dfrac{3\sqrt{5}}{5}+\dfrac{15\sqrt{5}}{5} \\\\= \dfrac{52\sqrt{5}}{5} .\end{array}
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