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: 48



Work Step by Step

Using the Distributive Property, the given expression, $ \sqrt{5}(\sqrt{15}-\sqrt{35}) ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{5}(\sqrt{15})-\sqrt{5}(\sqrt{35}) .\end{array} Using the properties of radicals, the expression above simplifies to \begin{array}{l}\require{cancel} \sqrt{5(15)}-\sqrt{5(35)} \\\\= \sqrt{75}-\sqrt{175} \\\\= \sqrt{25\cdot3}-\sqrt{25\cdot7} \\\\= \sqrt{(5)^2\cdot3}-\sqrt{(5)^2\cdot7} \\\\= 5\sqrt{3}-5\sqrt{7} .\end{array}
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