Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set: 59

Answer

$6\sqrt[4]{63}+4\sqrt[4]{35}-3\sqrt[4]{54}-2\sqrt[4]{30}$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $ (2\sqrt[4]{7}-\sqrt[4]{6})(3\sqrt[4]{9}+2\sqrt[4]{5}) ,$ is equivalent to \begin{array}{l}\require{cancel} (2\sqrt[4]{7})(3\sqrt[4]{9})+(2\sqrt[4]{7})(2\sqrt[4]{5})-(\sqrt[4]{6})(3\sqrt[4]{9})-(\sqrt[4]{6})(2\sqrt[4]{5}) \\\\= 2(3)\sqrt[4]{7(9)}+2(2)\sqrt[4]{7(5)}-3\sqrt[4]{6(9)}-2\sqrt[4]{6(5)} \\\\= 6\sqrt[4]{63}+4\sqrt[4]{35}-3\sqrt[4]{54}-2\sqrt[4]{30} .\end{array}
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