Chapter 5 - Number Theory and the Real Number System - 5.5 Real Numbers and Their Properties; Clock Addition - Exercise Set 5.5 - Page 308: 11

$\sqrt 2$

The $\sqrt 2$ is an irrational number because its decimal approximation never repeats, not does it terminate. Since the real numbers are made up by combining all the rational and irrational numbers, the $\sqrt 2$ is also real.