Elementary Algebra

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

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4: 28

Answer

$3\sqrt[]{5}-5\sqrt[]{3}$

Work Step by Step

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $ \sqrt[]{15}(\sqrt[]{3}-\sqrt[]{5}) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[]{15}(\sqrt[]{3})-\sqrt[]{15}(\sqrt[]{5}) \\\\= \sqrt[]{15(3)}-\sqrt[]{15(5)} \\\\= \sqrt[]{(5\cdot3)(3)}-\sqrt[]{(5\cdot3)(5)} \\\\= \sqrt[]{3^2\cdot5}-\sqrt[]{5^2\cdot3} \\\\= 3\sqrt[]{5}-5\sqrt[]{3} .\end{array}
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