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

To do: 

We have to give an example of each of two irrational numbers whose difference is an irrational number.

Solution:

A rational number can be expressed in either terminating decimal or non-terminating recurring decimals and an irrational number is expressed in non-terminating non-recurring decimals.

$\sqrt{2}$ is an irrational number.

This implies,

$5\sqrt{2}, 4\sqrt{2}$ are irrational numbers.

Therefore,

$(5\sqrt{2})-(4\sqrt{2})=(5-4)\sqrt{2}$

$=\sqrt{2}$.

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Updated on: 10-Oct-2022

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