College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises - Page 68: 74



Work Step by Step

$\bf{\text{Solution Outline:}}$ To add/subtract the given expression, $ \sqrt[4]{256x^5y^6}+\sqrt[4]{625x^9y^2} ,$ simplify first each radical term by extracting the factor that is a perfect power of the index. Then, combine the like radicals. $\bf{\text{Solution Details:}}$ Extracting the factors of each radicand that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[4]{256x^4y^4\cdot xy^2}+\sqrt[4]{625x^8\cdot xy^2} \\\\= \sqrt[4]{(4xy)^4\cdot xy^2}+\sqrt[4]{(5x^2)^4\cdot xy^2} \\\\= 4xy\sqrt[4]{xy^2}+5x^2\sqrt[4]{xy^2} .\end{array} Note that all variables are assumed to have positive values. Combining the like radicals results to \begin{array}{l}\require{cancel} (4xy+5x^2)\sqrt[4]{xy^2} .\end{array}
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