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: 64

Answer

$\dfrac{3-\sqrt{5}+3\sqrt{2}-\sqrt{10}}{4}$

Work Step by Step

Multiplying by the conjugate of the denominator, the rationalized-denominator form of the given expression, $ \dfrac{1+\sqrt{2}}{3+\sqrt{5}} ,$ is \begin{array}{l}\require{cancel} \dfrac{1+\sqrt{2}}{3+\sqrt{5}}\cdot\dfrac{3-\sqrt{5}}{3-\sqrt{5}} \\\\= \dfrac{1(3)+1(-\sqrt{5})+\sqrt{2}(3)+\sqrt{2}(-\sqrt{5})}{3^2-(\sqrt{5})^2} \\\\= \dfrac{3-\sqrt{5}+3\sqrt{2}-\sqrt{2(5)}}{9-5} \\\\= \dfrac{3-\sqrt{5}+3\sqrt{2}-\sqrt{10}}{4} .\end{array}
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