Chapter 9.8, Problem 35E

To determine

Tofind:If the given number is rational or irrational

Answer to Problem 35E

Irrational

Explanation of Solution

Given information:

  $\sqrt{32}$

Concept Used:

While solving a fraction, root or any numerical expression, if the final value is a terminating or repeating decimal, the expression is said to be rational but if the final value is nonterminating decimal, the expression is said to be irrational

Calculation:

  $\begin{array}{l}\sqrt{32}=\sqrt{16·2}\\ =\sqrt{4^2·2}\\ =4\sqrt{2}\\ =4\sqrt{2}\\ =4\left(\mathrm{1.41421356237.....}\right)\end{array}$

As $\sqrt{2}$ yields a non-terminating decimal. Therefore, we can say that $\sqrt{32}$ is irrational