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

Adding a rational number to an irrational number gives an irrational result; otherwise, subtracting the rational number from the result would make the irrational number rational. Multiplying an irrational number by a nonzero rational number also gives an irrational result, since dividing by that rational number would otherwise make the irrational number rational. Therefore, the result is always irrational, choice A.

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