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: 32

Answer

$31+11\sqrt[]{3}$

Work Step by Step

Using the FOIL method and the properties of radicals, the given expression, $ (\sqrt[]{3}+4)(\sqrt[]{3}+7) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[]{3}(\sqrt[]{3})+\sqrt[]{3}(7)+4(\sqrt[]{3})+4(7) \\\\= 3+7\sqrt[]{3}+4\sqrt[]{3}+28 \\\\= (3+28)+(7\sqrt[]{3}+4\sqrt[]{3}) \\\\= 31+11\sqrt[]{3} .\end{array}
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