Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set: 41

Answer

$4+3\sqrt{6}$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $ (2+\sqrt{6})(5-\sqrt{6}) ,$ is equivalent to \begin{array}{l}\require{cancel} 2(5)+2(-\sqrt{6})+\sqrt{6}(5)+\sqrt{6}(-\sqrt{6}) \\\\= 10-2\sqrt{6}+5\sqrt{6}-\sqrt{6(6)} \\\\= 10+3\sqrt{6}-\sqrt{(6)^2} \\\\= 10+3\sqrt{6}-6 \\\\= 4+3\sqrt{6} .\end{array}
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