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 - Page 539: 60



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: $\require{cancel}=\sqrt[3]{\dfrac{250x^5y^3}{2x^3}} \\=\sqrt[3]{\dfrac{125\cancel{250}\cancel{x^5}x^2y^3}{\cancel{2x^3}}} \\=\sqrt[3]{125x^2y^3}$ Factor the radicand so that at least one factor is a perfect square to obtain: $=\sqrt[3]{125y^3(x^2)} \\=\sqrt[3]{5^3y^3(x^2)} \\=\sqrt[3]{(5y)^3(x^2)}$ Simplify to obtain: $=5y\sqrt[3]{x^2}$
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