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: 72

Answer

$\dfrac{1}{\sqrt{15}+3}$

Work Step by Step

Multiplying by the conjugate of the numerator, the rationalized-numerator form of the given expression, $ \dfrac{\sqrt{15}-3}{6} ,$ is \begin{array}{l}\require{cancel} \dfrac{\sqrt{15}-3}{6}\cdot\dfrac{\sqrt{15}+3}{\sqrt{15}+3} \\\\= \dfrac{(\sqrt{15})^2-(3)^2}{6(\sqrt{15})+6(3)} \\\\= \dfrac{15-9}{6\sqrt{15}+18} \\\\= \dfrac{6}{6(\sqrt{15}+3)} \\\\= \dfrac{\cancel{6}}{\cancel{6}(\sqrt{15}+3)} \\\\= \dfrac{1}{\sqrt{15}+3} .\end{array}
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