Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 8 - Radical Functions - 8.2 Simplifying, Adding, and Subtracting Radicals - 8.2 Exercises: 61

Answer

$\color{blue}{(35x^2y^3-54x^2y^2)\sqrt[3]{z^2}}$

Work Step by Step

Factor each radicand so that at least one factor is a perfect cube, then then bring out the cube root of the perfect cube factors to obtain: $=7\sqrt[3]{5^3(x^2)^3(y^3)^3(z^2)}-9x^2y\sqrt[3]{6^3y^3(z^2)} \\=7(5x^2y^3)\sqrt[3]{z^2}-9x^2y(6y)\sqrt[3]{z^2} \\=35x^2y^3\sqrt[3]{z^2}-54x^2y^2\sqrt[3]{z^2}$ Combine like terms to obtain: $=\color{blue}{(35x^2y^3-54x^2y^2)\sqrt[3]{z^2}}$
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