Q: Is the product of a rational number and an irrational number always irrational?

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The product of an irrational number and a rational number, both nonzero, is always irrational

Yes, always.

Yes, it is possible only if an irrational number is multiplied with 0.

It is always an irrational number.

The question is nonsense because the product of two rational numbers is never irrational.

Related questions

The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.

Such a product is always irrational - unless the rational number happens to be zero.

No.A rational times an irrational is never rational. It is always irrational.

It is always irrational.

Provided that the rational number is not 0, the product is irrational.

Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)

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.

The product of an irrational number and a rational number, both nonzero, is always irrational

No, but the only exception is if the rational number is zero.

It is always rational.

Yes, always.