Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.3 - Multiplying and Simplifying Radical Expressions - Exercise Set - Page 531: 73


$2x^2 \sqrt {10x}$

Work Step by Step

Apply product rule: $\sqrt[n] p \sqrt[n] q=\sqrt[n]{pq}$ Here, $n$ refers as index. $\sqrt {5x^3} \sqrt[n] {8x^2}=\sqrt {(5x^3) (8x^2)}= \sqrt{40 x^5}$ The radical $\sqrt{40 x^5}$ can be further simplified by using product rule again. Such as: $\sqrt{40 x^5}=\sqrt {(4x^4) (10x)}=\sqrt {(2x^2)^2 (10x)}=2x^2 \sqrt {10x}$
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