Question

Give an example of two irrational numbers to show that their sum is an irrational number.

Answer 1

Irrational numbers:

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

Assume that the two irrational numbers are,

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

On adding these two we get

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

Where , $2\sqrt{5}$ is again an irrational number

Therefore , the two irrational numbers to show that their sum is an irrational number are $\sqrt{5}+\sqrt{3}$and $\sqrt{5}-\sqrt{3}$.