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: 60

Answer

$8\sqrt[3]{21}+20\sqrt[3]{18}+2\sqrt[3]{70}+5\sqrt[3]{60}$

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, $ (4\sqrt[3]{3}+\sqrt[3]{10})(2\sqrt[3]{7}+5\sqrt[3]{6}) ,$ is equivalent to \begin{array}{l}\require{cancel} (4\sqrt[3]{3})(2\sqrt[3]{7})+(4\sqrt[3]{3})(5\sqrt[3]{6})+(\sqrt[3]{10})(2\sqrt[3]{7})+(\sqrt[3]{10})(5\sqrt[3]{6}) \\\\= 4(2)\sqrt[3]{3(7)}+4(5)\sqrt[3]{3(6)}+2\sqrt[3]{10(7)}+5\sqrt[3]{10(6)} \\\\= 8\sqrt[3]{21}+20\sqrt[3]{18}+2\sqrt[3]{70}+5\sqrt[3]{60} .\end{array}
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