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 - 10.3 Multiplying Radical Expressions - 10.3 Exercise Set - Page 647: 68



Work Step by Step

Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression, $ 3\sqrt{5a^7}\cdot2\sqrt{15a^3} ,$ is equivalent to \begin{array}{l}\require{cancel} 3\sqrt{5a^7}\cdot2\sqrt{15a^3} \\\\= 3(2)\sqrt{5a^7(15a^3)} \\\\= 6\sqrt{75a^{10}} .\end{array} Extracting the factor that is a perfect power of the index (all radicands are assumed positive), then \begin{array}{l}\require{cancel} 6\sqrt{75a^{10}} \\\\= 6\sqrt{25a^{10}\cdot3} \\\\= 6\sqrt{(5a^{5})^2\cdot3} \\\\= 6\cdot5a^{5}\sqrt{3} \\\\= 30a^{5}\sqrt{3} .\end{array}
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