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 - Page 634: 60



Work Step by Step

Simplify each radical: $=4m^3\sqrt{25m^4n^6p^2(6mp)}-5n^2\sqrt{100m^{10}n^2p^2(6mp)} \\=4m^3\sqrt{5^2(m^2)^2(n^3)^2p^2(6mp)}-5n^2\sqrt{10^2(m^5)^2n^2p^2(6mp)} \\=4m^3(5m^2n^3p)\sqrt{6mmp} - 5n^2(10m^5np)\sqrt{6mp} \\=20m^5n^3p\sqrt{6mp} - 50m^5n^3p\sqrt{6mp}$ Combine like terms to obtain: $=(20-50)m^5n^3p\sqrt{6mp} \\=\color{blue}{-30m^5n^3p\sqrt{6mp}}$
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