Question

Question 8
The product of a non – zero rational and an irrational number is

A) Always irrational
B) Always rational
C) Rational or irrational
D) One

Answer 1

Consider an example,
$\frac{3}{4}\times \sqrt{2}=\frac{3\sqrt{2}}{4}$

Here, $\frac{3}{4}$ is the non zero rational number, and $\sqrt{2}$ is the irrational number.

Their product, $\frac{3\sqrt{2}}{4}$ is irrational.

This is going to be true no matter what the non-zero rational or the irrational number is since the irrationality of the number is not removed.

Thus, we can say that the product of a non – zero rational and an irrational number is always irrational.