College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises - Page 68: 83



Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ (3\sqrt{2}+\sqrt{3})(2\sqrt{3}-\sqrt{2}) ,$ use the FOIL method. $\bf{\text{Solution Details:}}$ 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{2}(2\sqrt{3})+3\sqrt{2}(-\sqrt{2})+\sqrt{3}(2\sqrt{3})+\sqrt{3}(-\sqrt{2}) \\\\= 3(2)\sqrt{2(3)}-3\sqrt{2(2)}+2\sqrt{3(3)}-\sqrt{3(2)} \\\\= 6\sqrt{6}-3\sqrt{4}+2\sqrt{9}-\sqrt{6} \\\\= 6\sqrt{6}-3\sqrt{(2)^2}+2\sqrt{(3)^2}-\sqrt{6} \\\\= 6\sqrt{6}-3(2)+2(3)-\sqrt{6} \\\\= 6\sqrt{6}-6+6-\sqrt{6} \\\\= 6\sqrt{6}-\sqrt{6} \\\\= 5\sqrt{6} .\end{array}
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