Chapter 9.4, Problem 40E

To determine

Whether $\sqrt{2}$ is rational or irrational number

Answer to Problem 40E

  $\sqrt{2}$ is a non-terminating and non-repeating number, hence, it is an irrational number.

Explanation of Solution

Set of rational numbers = All the real numbers which can be written in terms of a fraction

Set of irrational numbers = All the real numbers which cannot be written in terms of a fraction (non-terminating, non-repeating)

  $\begin{array}{l}\frac{2\sqrt{2}}{2}=\sqrt{2}\\ \sqrt{2}=\mathrm{1.41421356237....}\end{array}$

As $\sqrt{2}$ equals a non-terminating and non-repeating number, hence, it is an irrational number.