Intermediate Algebra for College Students (7th Edition)

Published by Pearson

Chapter 7 - Section 7.4 - Adding, Subtracting, and Dividing Radical Expressions - Exercise Set: 22

Answer

$5y\sqrt[3]{3x}$

Work Step by Step

Simplify each radical by factoring the radicand so that at least one factor is a perfect cube to obtain: $=\sqrt[3]{8y^3(3x)} + y\sqrt[3]{27(3x)} \\=\sqrt[3]{(2y)^3(3x)} + y\sqrt[3]{(3^3)(3x)} \\=2y\sqrt[3]{3x} + y(3)\sqrt[3]{3x} \\=2y\sqrt[3]{3x} + 3y\sqrt[3]{3x}$ RECALL: The distributive property states that for any real numbers a, b, and c: (1) $ac + bc = (a+b)c$ (2) $ac-bc=(a-b)c$ Use the rule (1) above to combine like terms and obtain: $=(2y+3y)\sqrt[3]{3x} \\=5y\sqrt[3]{3x}$

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