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: 18

Answer

$\sqrt{15}-2\sqrt{3}+3\sqrt{5}-6$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ (\sqrt{3}+3)(\sqrt{5}-2) ,$ 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{3}(\sqrt{5})-\sqrt{3}(2)+3(\sqrt{5})+3(-2) \\\\= \sqrt{3}(\sqrt{5})-2\sqrt{3}+3\sqrt{5}-6 .\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{3(5)}-2\sqrt{3}+3\sqrt{5}-6 \\\\= \sqrt{15}-2\sqrt{3}+3\sqrt{5}-6 .\end{array}
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