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

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KollegeApply · Accepted Answer

The product of a non-zero rational and an irrational number is always irrational. Explanation: Consider an example, $\frac{3}{4}$ xx sqrt2 = (3sqrt2)/4 Here, $\frac{3}{4}$ 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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