Question

Given an example where the difference of two irrational numbers is a rational number.

Answer 1

Rational Number: Any number which can be expressed in the form of $\frac{p}{q}$, where p and q are integers, $q\ne 0$.

Ex. $2,\frac{1}{3},\frac{6}{11},...$

Irrational Number: Any number which cannot be expressed in the form of $\frac{p}{q}$, where p and q are integers, $q\ne 0$.

Ex. $\sqrt{2},\sqrt{5},\sqrt{11},...$

We have to show that the difference of two irrational numbers is a rational number.

Let two irrational numbers be .$5+\sqrt{3}\mathrm{and}4+\sqrt{3}$.

$\left(5+\sqrt{3}\right)-\left(4+\sqrt{3}\right)=5+\sqrt{3}-4-\sqrt{3}=1$

which is a rational number.

Hence, examples of two irrational numbers are $5+\sqrt{3}\mathrm{and}4+\sqrt{3}$.