Intermediate Algebra (12th Edition)

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

Chapter 7 - Section 7.4 - Adding and Subtracting Radical Expressions - 7.4 Exercises: 43

Answer

$2\sqrt{2}-2$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ \sqrt{8}-\dfrac{\sqrt{64}}{\sqrt{16}} ,$ simplify first each term by using the laws of radicals and by extracting the factor of the radicand that is a perfect power of the index. Then combine the like radicals. $\bf{\text{Solution Details:}}$ Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt{8}-\sqrt{\dfrac{64}{16}} \\\\= \sqrt{8}-\sqrt{4} .\end{array} Rewriting the radicand as an expression that contains a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt{4\cdot2}-\sqrt{4} \\\\= \sqrt{(2)^2\cdot2}-\sqrt{(2)^2} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 2\sqrt{2}-2 .\end{array}
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