Intermediate Algebra (12th Edition)

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

Chapter 7 - Summary Exercises - Performing Operations with Radicals and Rational Exponents: 6

Answer

$7-\sqrt{14}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ \sqrt{7}(\sqrt{7}-\sqrt{2}) ,$ use the Distributive Property and the laws of radicals. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} \sqrt{7}(\sqrt{7})+\sqrt{7}(-\sqrt{2}) \\\\= (\sqrt{7})^2-\sqrt{7}(\sqrt{2}) \\\\= 7-\sqrt{7}(\sqrt{2}) .\end{array} Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel} 7-\sqrt{7(2)} \\\\= 7-\sqrt{14} .\end{array}
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