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# The product of a non-zero rational and an irrational number is

**(A)** always irrational

**(B)** always rational

**(C)** rational or irrational

**(D)** one

To do:

We have to find the correct option.

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 and $2$ is a rational number.

Therefore,

$2\times\sqrt{2}=2\sqrt{2}$which is an irrational number.

Hence, the product of a non-zero rational and an irrational number is always irrational.

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