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 - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 37

Answer

$\sqrt[]{2ab}$

Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{\sqrt[]{100ab}}{5\sqrt[]{2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{5}\sqrt[]{\dfrac{100ab}{2}} \\\\= \dfrac{1}{5}\sqrt[]{50ab} \\\\= \dfrac{1}{5}\sqrt[]{25\cdot2ab} \\\\= \dfrac{1}{5}\sqrt[]{(5)^2\cdot2ab} \\\\= \dfrac{1}{5}\cdot5\sqrt[]{2ab} \\\\= \sqrt[]{2ab} .\end{array} * Note that it is assumed that all variables represent positive numbers.
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