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: 36

Answer

$4+\sqrt[]{10}+4\sqrt{3}+\sqrt{30}$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the Distributive Property, and the properties of radicals, the given expression, $ (\sqrt[]{2}+\sqrt{6})(\sqrt[]{8}+\sqrt{5}) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[]{2}(\sqrt[]{8})+\sqrt[]{2}(\sqrt{5})+\sqrt{6}(\sqrt[]{8})+\sqrt{6}(\sqrt{5}) \\\\= \sqrt[]{16}+\sqrt[]{10}+\sqrt{48}+\sqrt{30} \\\\= \sqrt[]{(4)^2}+\sqrt[]{10}+\sqrt{16\cdot3}+\sqrt{30} \\\\= \sqrt[]{(4)^2}+\sqrt[]{10}+\sqrt{(4)^2\cdot3}+\sqrt{30} \\\\= 4+\sqrt[]{10}+4\sqrt{3}+\sqrt{30} .\end{array}
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