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

Answer

$30a^{5}\sqrt{3}$

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}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.