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 7.4 - Adding, Subtracting, and Dividing Radical Expressions - Exercise Set: 59

Answer

$2xy$

Work Step by Step

RECALL: (1) The quotient rule: $\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}}$ where $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$ (2) $\dfrac{a^m}{a^n} = a^{m-n}, a \ne =0$ Use the quotient rule above to obtain: $\require{cancel}=\sqrt[3]{\dfrac{24x^3y^5}{3y^2}} \\=\sqrt[3]{\dfrac{8\cancel{24}x^3\cancel{y^5}y^3}{\cancel{3y^2}}} \\=\sqrt[3]{8x^3y^3}$ Factor the radicand so that at least one factor is a perfect square to obtain: $=\sqrt[3]{2^3x^3y^3} \\=\sqrt[3]{(2xy)^3}$ Simplify to obtain: $=2xy$
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