Chapter 1.3, Problem 7LC

To determine

To find: the reason to tell whether $\sqrt{100}$ is rational or irrational.

Answer to Problem 7LC

  $\sqrt{100}$ is rational number.

Explanation of Solution

Given:

  $\sqrt{100}$ .

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.

Calculation:

Consider the number:

  $\sqrt{100}$ .

Determine whether the number is rational or irrational.

It is known that $\sqrt{100}=10.$

The numbers of the form $\frac{a}{b}$ , where $a\text{ and }b$ are integer and $b\ne 0$ are called rational numbers.

  $Q=\left\{\frac{a}{b};a\in z,b\in z,b\ne 0\right\}$ is set of rational numbers.

The number $10$ can be written as a ratio of two integers, $\frac{10}{1}\left(1\ne 0\right)$ .

Thus, $10$ is rational number.

Hence, $\sqrt{100}$ is rational number.