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: 71

Answer

$\dfrac{1}{\sqrt{5}-1}$

Work Step by Step

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