Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.5 - Multiplying and Dividing Radical Expressions - 7.5 Exercises - Page 475: 20

Answer

$\sqrt{39}+\sqrt{143}-\sqrt{21}-\sqrt{77}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ (\sqrt{13}-\sqrt{7})(\sqrt{3}+\sqrt{11}) ,$ use FOIL and the properties of radicals. $\bf{\text{Solution Details:}}$ Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the expression above is equivalent to\begin{array}{l}\require{cancel} \sqrt{13}(\sqrt{3})+\sqrt{13}(\sqrt{11})-\sqrt{7}(\sqrt{3})-\sqrt{7}(\sqrt{11}) .\end{array} Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel} \sqrt{13(3)}+\sqrt{13(11)}-\sqrt{7(3)}-\sqrt{7(11)} \\\\= \sqrt{39}+\sqrt{143}-\sqrt{21}-\sqrt{77} .\end{array}
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