Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.5 - Multiplying and Dividing Radical Expressions - 7.5 Exercises: 100

Answer

$2+\sqrt{5}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the the given expression, $ \dfrac{24+12\sqrt{5}}{12} ,$ find the $GCF$ of all the terms. Then, express all terms as factors using the $GCF.$ Finally, cancel the $GCF$ in all the terms. $\bf{\text{Solution Details:}}$ The $GCF$ of the coefficients of the terms, $\{ 24,12,12 \},$ is $ 12 $ since it is the highest number that can divide all the given coefficients. Writing the given expression as factors using the $GCF$ results to \begin{array}{l}\require{cancel} \dfrac{12\cdot2+12\cdot1\sqrt{5}}{12\cdot1} .\end{array} Cancelling the $GCF$ in every term results to \begin{array}{l}\require{cancel} \dfrac{\cancel{12}\cdot2+\cancel{12}\cdot1\sqrt{5}}{\cancel{12}\cdot1} \\\\= \dfrac{2+1\sqrt{5}}{1} \\\\= 2+\sqrt{5} .\end{array}
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