Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set: 47

Answer

$5ab\sqrt b$

Work Step by Step

$\sqrt (25a^{2}b^{3})=\sqrt (25\times a^{2}\times b^{2}\times b)=\sqrt 25\times \sqrt (a^{2})\times \sqrt (b^{2})\times\sqrt b=5ab\sqrt b$ We know that $\sqrt 25=5$, because $5^{2}=25$. We know that $\sqrt (a^{2})=a$, because $(a)^{2}=a^{2}$, and also that $\sqrt (b^{2})=b$, because $(b)^{2}=b^{2}$.
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