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: 62

Answer

$\color{blue}{-28ab^2c^3\sqrt[3]{5}}$

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: $=2\sqrt[3]{216a^3b^6c^9(5)}-8abc\sqrt[3]{125b^3c^6(5)} \\=2\sqrt[3]{6^3a^3(b^2)^3(c^3)^3(5)}-8abc\sqrt[3]{5^3b^3(c^2)^3(5)} \\=2(6ab^2c^3)\sqrt[3]{5}-8abc(5bc^2)\sqrt[3]{5} \\=12ab^2c^3\sqrt[3]{5} -40ab^2c^3\sqrt[3]{5}$ Combine like terms to obtain: $=(12ab^2c^3-40ab^2c^3)\sqrt[3]{5} \\=\color{blue}{-28ab^2c^3\sqrt[3]{5}}$
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