Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.4 The Irrational Numbers - Concept and Vocabulary Check - Page 296: 9


$\sqrt 7$

Work Step by Step

A fraction that is equivalent to $\sqrt \frac{2}{7}$ can be found by rationalizing the denominator. This means that we multiply both the numerator and denominator of the fraction by the denominator of the fraction in question, keeping the number under a radical sign. So, rationalizing the denominator, we get: $\sqrt \frac{2}{7}$ $\times$ $\sqrt \frac{7}{7}$ Note: See how the second fraction uses the denominator of 7, but keeps the entire unit under the radical. This gives us a numerator of: $\sqrt 14$ (2 x 7 = 14) And a denominator of $\sqrt 49$ since 7 x 7 = 49 Since $\sqrt 49$ = 7, we end up with $\frac{\sqrt 14}{7}$ This is our equivalent fraction with the denominator rationalized.
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