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: 52

Answer

$2m^3n^2\sqrt{6n}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ \sqrt{24m^6n^5} ,$ use the laws of exponents to simplify the radicand. Then, find a factor of the radicand that is a perfect power of the index. Finally, extract the root of the factor that is a perfect power of the root. $\bf{\text{Solution Details:}}$ Factoring the expression that is a perfect power of the index and then extracting the root result to \begin{array}{l}\require{cancel} \sqrt{4m^6n^4\cdot6n} \\\\= \sqrt{(2m^3n^2)^2\cdot6n} \\\\= |2m^3n^2|\sqrt{6n} .\end{array} Since all variables are assumed to be positive, then, \begin{array}{l}\require{cancel} 2m^3n^2\sqrt{6n} .\end{array}
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