Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises - Page 460: 101


$4\sqrt 3$

Work Step by Step

We know from the radical form of $a^{\frac{m}{n}}$ that $a^{\frac{m}{n}}=\sqrt[n] a^{m}$ (where the indicated root is a real number). Therefore, $\sqrt[4] 48^{2}=48^{\frac{2}{4}}=48^{\frac{1}{2}}=\sqrt 48$ $\sqrt 48=\sqrt (16\times3)=\sqrt 16\times\sqrt 3=4\sqrt 3$
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