Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set: 76

Answer

$\dfrac{1}{\sqrt{10}-2\sqrt{2}}$

Work Step by Step

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