Intermediate Algebra (6th Edition)

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

Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set - Page 445: 71

Answer

$\dfrac{6x^2y^3}{\sqrt[]{6z}}$

Work Step by Step

Rationalizing the numerator of $ \sqrt[]{\dfrac{18x^4y^6}{3z}} $ results to \begin{array}{l} \sqrt[]{\dfrac{9x^4y^6\cdot2}{3z}} \\\\= 3x^2y^3\sqrt[]{\dfrac{2}{3z}} \\\\= 3x^2y^3\sqrt[]{\dfrac{2}{3z}} \cdot \sqrt[]{\dfrac{2}{2}} \\\\= 3x^2y^3\sqrt[]{\dfrac{4}{6z}} \\\\= \dfrac{3x^2y^3\cdot2}{\sqrt[]{6z}} \\\\= \dfrac{6x^2y^3}{\sqrt[]{6z}} .\end{array}
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