Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - Chapter 9 Review Problem Set: 46

Answer

$-18-\sqrt{5}$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the Distributive Property, and the properties of radicals, the given expression, $ (3+2\sqrt{5})(4-3\sqrt{5}) ,$ simplifies to \begin{array}{l}\require{cancel} 3(4)+3(-3\sqrt{5})+2\sqrt{5}(4)+2\sqrt{5}(-3\sqrt{5}) \\\\= 12-9\sqrt{5}+8\sqrt{5}-6(5) \\\\= 12-9\sqrt{5}+8\sqrt{5}-30 \\\\= (12-30)+(-9\sqrt{5}+8\sqrt{5}) \\\\= -18-\sqrt{5} .\end{array}
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