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 - 8.3 Multiplying and Dividing Radicals - 8.3 Exercises - Page 642: 19

Answer

$14x^3y\sqrt[3] {20y^2}$

Work Step by Step

First, we have to make sure that the indices are the same, which they are, in this exercise. We now multiply the radicands and the coefficients: $2x^2 • 7y\sqrt[3] {5x^2y • 4xy}$ Multiply the constants and add like variables: $14x^2y\sqrt[3] {20x^3y^2}$ Rewrite the radicand as the product of two factors. One of the factors should be such that we can take its cube root to remove it from under the radical sign: $14x^2y\sqrt[3] {20x^3y^2}$ Take the cube roots of the factors in the radicand: $14x^2y • x\sqrt[3] {20y^2}$ Multiply coeffients together: $14x^3y\sqrt[3] {20y^2}$
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