Intermediate Algebra (12th Edition)

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

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 72

Answer

$13s^2t^{5}\sqrt{s}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ \sqrt{169s^5t^{10}} ,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers. $\bf{\text{Solution Details:}}$ Expressing the radicand of the expression above with a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt{169s^4t^{10}\cdot s} \\\\= \sqrt{(13s^2t^{5})^2\cdot s} \\\\= 13s^2t^{5}\sqrt{s} .\end{array}
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