College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.4 - Rational Exponents and Radicals - P.4 Exercises - Page 30: 86


(a) $\displaystyle 4\sqrt{3}$ (b) $\displaystyle \frac{2\sqrt{15}}{5}$ (c) $\displaystyle \frac{8\sqrt[3]{5}}{5}$

Work Step by Step

(a) $\displaystyle \frac{12}{\sqrt{3}}=\frac{12}{\sqrt{3}} \displaystyle \frac{\sqrt{3}}{\sqrt{3}}=\frac{12\sqrt{3}}{3}=4\sqrt{3}$ (b)$\displaystyle \sqrt{\frac{12}{5}}=\frac{\sqrt{12}}{\sqrt{5}} \displaystyle=\frac{\sqrt{12}}{\sqrt{5}} \displaystyle \frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{60}}{5}=\frac{2\sqrt{15}}{5}$ (c) $\displaystyle \frac{8}{\sqrt[3]{5^{2}}}=\frac{8}{5^{2/3}} \displaystyle \frac{5^{1/3}}{5^{1/3}}=\frac{8\sqrt[3]{5}}{5}$
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