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: 49

Answer

$3x$

Work Step by Step

RECALL: 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 $b\ne0$ Use the rule above to obtain: $\require{cancel}=\sqrt{\dfrac{54x^3}{6x}} \\=\sqrt{\dfrac{\cancel{54}9\cancel{x^3}x^2}{\cancel{6x}}} \\=\sqrt{9x^2} \\=\sqrt{(3x)^2}$ Simplify to obtain: $=3x$
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