Question

Classify the following as rational number and irrational number: $-7-\sqrt{3}$

Answer 1

Definition:

1. Rational number: A rational number is a number that is 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 $q\ne 0$.

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

Given number is $-7-\sqrt{3}$.

Here, -7 is a rational number and is $\sqrt{3}$ an irrational number.

Thus, the difference of a rational and an irrational number is an irrational number.

Hence, $-7-\sqrt{3}$ is an irrational number.