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 - Page 433: 48


$3x^{2}y^{3}\sqrt (xy)$

Work Step by Step

$\sqrt (9x^{5}y^{7})=\sqrt (9\times x^{4}\times x \times y^{6}\times y)=\sqrt 9\times \sqrt (x^{4})\times \sqrt x \times \sqrt (y^{6})\times \sqrt y$ Further simplification: $3x^{2}y^{3}(\sqrt x\times\sqrt y)=3x^{2}y^{3}\sqrt (xy)$ We know that $\sqrt 9=3$, because $3^{2}=9$. We know that $\sqrt (x^{4})=x^{2}$, because $(x^{2})^{2}=x^{2\times2}=x^{4}$ and also that $\sqrt (y^{6})=y^{3}$, because $(y^{3})^{2}=y^{3\times2}=y^{6}$
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