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: 102


$5\sqrt 2$

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, $\sqrt[4] 50^{2}=50^{\frac{2}{4}}=50^{\frac{1}{2}}=\sqrt 50$ $\sqrt 50=\sqrt (25\times2)=\sqrt 25\times\sqrt 2=5\sqrt 2$
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