Question

Give an example of two irrational numbers to show that their difference is a rational number.

Answer 1

Irrational numbers:

Irrational numbers are the number having non-terminating and non- recurring decimals.

Let us assume the two irrational numbers be

$5+\sqrt{2}$ and $3+\sqrt{2}$

On subtracting these numbers we get

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

Where, $2$ is rational number

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