Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.7 Radical Expressions - R.7 Exercises: 82

Answer

$\color{blue}{(4xy+5x^2)\sqrt[4]{xy^2}}$

Work Step by Step

Simplify each radical. Factor the radicand so that one factor is a perfect fourth power, then bring out the fourth root of the perfect fourth power factor to obtain: $=\sqrt[4]{256x^4y^4(xy^2)}+\sqrt[4]{625x^8(xy^2)} \\=\sqrt[4]{4^4x^4y^4(xy^2)} + \sqrt[4]{5^4(x^2)^4(xy^2)} \\=4xy\sqrt[4]{xy^2}+5x^2\sqrt[4]{xy^2}$ Combine like terms to obtain: $\\=\color{blue}{(4xy+5x^2)\sqrt[4]{xy^2}}$
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