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Question
The product of a non-zero rational and an irrational number is ______.
Options
Always irrational
Always rational
Rational or Irrational
One
Solution
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.
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