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: 31

Answer

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

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ (3\sqrt{x}-\sqrt{5})(2\sqrt{x}+1) ,$ use FOIL and the laws 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} 3\sqrt{x}(2\sqrt{x})+3\sqrt{x}(1)-\sqrt{5}(2\sqrt{x})-\sqrt{5}(1) \\\\= 3(2)(\sqrt{x})^2+3\sqrt{x}-1(2)\sqrt{5}(\sqrt{x})-\sqrt{5} \\\\= 6x+3\sqrt{x}-2\sqrt{5}(\sqrt{x})-\sqrt{5} .\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} 6x+3\sqrt{x}-2\sqrt{5(x)}-\sqrt{5} \\\\= 6x+3\sqrt{x}-2\sqrt{5x}-\sqrt{5} .\end{array}
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