No, but the only exception is if the rational number is zero.
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The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
No.A rational times an irrational is never rational. It is always irrational.
Not if the rational number is zero. In all other cases, the product is irrational.
The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.
It is always rational.