Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set - Page 439: 40



Work Step by Step

Using the properties of radicals, the given expression, $ \dfrac{\sqrt[]{99}}{5x}-\sqrt[]{\dfrac{44}{x^2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[]{9\cdot11}}{5x}-\sqrt[]{\dfrac{4}{x^2}\cdot11} \\\\= \dfrac{\sqrt[]{(3)^2\cdot11}}{5x}-\sqrt[]{\left( \dfrac{2}{x}\right)^2\cdot11} \\\\= \dfrac{3\sqrt[]{11}}{5x}-\dfrac{2\sqrt[]{11}}{x} \\\\= \dfrac{3\sqrt[]{11}-5(2\sqrt[]{11})}{5x} \\\\= \dfrac{3\sqrt[]{11}-10\sqrt[]{11}}{5x} \\\\= \dfrac{-7\sqrt[]{11}}{5x} .\end{array} Note that variables are assumed to have positive values.
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