Question

Classify the following numbers as rational or irrational :

$\sqrt{23}$

Answer 1

A rational and irrational number.

Any decimal representation that is terminating or non-terminating but repeating of digits after the decimal point will be a rational number.

Any decimal representation that is non-terminating and non-recurring, will be an irrational number.

$\because \sqrt{23}=4.795831523.....$

It is observed that the given number is non-terminating and non-recurring.

Hence, $\sqrt{23}$ is an irrational number.