Answer :

Given: x is rational number and y is irrational number.

Yes, xy is necessarily an irrational number.


Example: Let x = 2, which is rational.


Let y = √2, which is irrational.


Then, x × y = 2 × √2 = 2√2, which is again irrational.


Also, consider the case when x = 0.


Then xy = 0, which is rational.


Product of a rational and an irrational number is always irrational, only if the rational number is not zero.


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