Question

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

Answer 1

Explanation:

Let the two irrational numbers be $5+\sqrt{2}$ and $3+\sqrt{2}$.

Difference of the numbers:

$$\begin{gathered} 5+\sqrt{2}-(3+\sqrt{2}) \\ =5+\sqrt{2}-3-\sqrt{2} \\ =5-3 \\ =2 \end{gathered}$$

Since $2$ is a rational number.

Therefore, the two irrational numbers whose difference is a rational number are $5+\sqrt{2}$ and $3+\sqrt{2}$.