Question

Give an example of two irrational numbers whose sum is a rational number.

Answer 1

Example for the required condition :

Irrational numbers are a type of real numbers which cannot be expressed in $\frac{p}{q}$ form where $p$ and $q$ are integers and $q\ne 0$.

Consider the irrational numbers $\sqrt{5}$ and $-\sqrt{5}$ .

Their sum is $\sqrt{5}+\left(-\sqrt{5}\right)=0$ i.e. a rational number.

Hence, $\sqrt{5}$ and $-\sqrt{5}$ are examples of two irrational numbers whose sum is a rational number.