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: 54

Answer

$\dfrac{16\sqrt{10}}{5}$

Work Step by Step

Using the properties of radicals, the given expression, $ 3\sqrt{10}+\sqrt{\dfrac{2}{5}} ,$ simplifies to \begin{array}{l}\require{cancel} 3\sqrt{10}+\sqrt{\dfrac{2}{5}\cdot\dfrac{5}{5}} \\\\= 3\sqrt{10}+\sqrt{\dfrac{10}{25}} \\\\= 3\sqrt{10}+\dfrac{\sqrt{10}}{\sqrt{25}} \\\\= 3\sqrt{10}+\dfrac{\sqrt{10}}{5} \\\\= \dfrac{15\sqrt{10}}{5}+\dfrac{\sqrt{10}}{5} \\\\= \dfrac{16\sqrt{10}}{5} .\end{array}
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