Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Prerequisites - P.2 - Exponents and Radicals - Exercises - Page 25: 44


(a) $\frac{2\sqrt[3] 2}{3}$ (b) $\frac{5\sqrt 3}{2}$

Work Step by Step

(a) $\sqrt[3] {\frac{16}{27}}=\frac{\sqrt[3] {16}}{\sqrt[3] {27}}=\frac{\sqrt[3] {8\times2}}{\sqrt[3] {3^3}}=\frac{\sqrt[3] {2^3\times2}}{3}=\frac{2\sqrt[3] 2}{3}$ (b) $\sqrt {\frac{75}{4}}=\frac{\sqrt {75}}{\sqrt 4}=\frac{\sqrt {25\times3}}{\sqrt {2^2}}=\frac{\sqrt {5^2\times3}}{2}=\frac{5\sqrt 3}{2}$
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