Chapter 1.3, Problem 8LC

To determine

To find: the reason to tell whether $\sqrt{0.29}$ is rational or irrational.

Answer to Problem 8LC

  $\sqrt{0.29}$ is an irrational number.

Explanation of Solution

Given:

  $\sqrt{0.29}$ .

Concept used:

Rational number are those number which is in the form of $\frac{p}{q}$ where $q\ne 0$ .

In the case of decimal expansion of a rational number either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over.

Moreover, any repeating or terminating decimal represents a rational number.

Irrational number is opposite to the rational number which means it is non-terminating number.

Calculation:

Consider the number:

  $\sqrt{0.29}$ ,

Determine whether the number is rational or irrational.

Use calculator to find the value of $\sqrt{0.29}$ .

  $\sqrt{0.29}=\mathrm{0.53851....}$

A number which can be expressed in decimal form is expressible as a non-terminating and mom-repeating decimal is called an irrational number.

So, $\sqrt{0.29}$ is non repeating, non-terminating number.

Thus, $\sqrt{0.29}$ is an irrational number.

Hence, $\sqrt{0.29}$ is an irrational number.