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: 35

Answer

$3\sqrt[]{2}+2\sqrt[]{6}+6+4\sqrt{3}$

Work Step by Step

Using the FOIL method and the properties of radicals, the given expression, $ (\sqrt[]{3}+\sqrt{6})(\sqrt[]{6}+\sqrt{8}) ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[]{3}(\sqrt[]{6})+\sqrt[]{3}(\sqrt{8})+\sqrt{6}(\sqrt[]{6})+\sqrt{6}(\sqrt{8}) \\\\= \sqrt[]{18}+\sqrt[]{24}+6+\sqrt{48} \\\\= \sqrt[]{9\cdot2}+\sqrt[]{4\cdot6}+6+\sqrt{16\cdot3} \\\\= \sqrt[]{(3)^2\cdot2}+\sqrt[]{(2)^2\cdot6}+6+\sqrt{(4)^2\cdot3} \\\\= 3\sqrt[]{2}+2\sqrt[]{6}+6+4\sqrt{3} .\end{array}
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