Question

Classify the following as rational number and irrational number: $\sqrt{7}$

Answer 1

Definition:

1. Rational number: A rational number is a number that can expressed as $\frac{p}{q}$, where p and q are integers, and $q\ne 0$.

Ex. $2,\frac{1}{4},\frac{11}{7},...$

2. Irrational number: An irrational number is a number that cannot be expressed as $\frac{p}{q}$, where p and q are integers, and $q\ne 0$ as it has a non-terminating and non-recurring decimal expansion.

Ex.$\sqrt{2},\sqrt{3},\sqrt{11},...$

Given number is $\sqrt{7}$.

Here, $\sqrt{7}=2.6457...$

As this is a non-terminating and non-recurring decimal expansion, it is an irrational number.