Question

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

Options

• Always irrational

• Always rational

• Rational or Irrational

• One

Answer 1

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

Explanation:

Consider an example,

`3/4 xx sqrt2 = (3sqrt2)/4`

Here, `3/4` is the non zero rational number, and `sqrt2` is the irrational number.

Their product, `(3sqrt2)/4` is irrational.

Since the irrationality of the number remains, this will hold true regardless of the non-zero rational or irrational number.

Therefore, we can state that an irrational number multiplied by a non-zero rational number is always irrational.