Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.2 - Exponents and Radicals - 1.2 Exercises - Page 21: 5

Answer

Rationalizing a denominator means eliminating the radical in the denominator. $\frac{1}{\sqrt 3}$=$\frac{1}{\sqrt 3}$$\times$$\frac{\sqrt 3}{\sqrt 3}$= $\frac{\sqrt 3}{3}$

Work Step by Step

If we have $\frac{1}{\sqrt[n]{a^{m}}}$ we should multiply both numerator and denominator by $\sqrt[n]{a^{n-m}}$ which is equivalent to multiplying by one. so for $\sqrt[2]{3^1}$ we should multiply both numerator and denominator by $\sqrt[2]{3^{2-1}} = \sqrt{3}$. After that, we obtain a standard form.
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