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Yes, except in the degenerate case where the rational number is 0, in which case the product is also 0, a rational result.

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

What is the product of rational and irrational number?

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


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

No. 0 is a rational number and the product of 0 and any irrational number will be 0, a rational. Otherwise, though, the product will always be irrational.


Is the product of a rational number and an irrational number rational or irrational?

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


Is the product of a rational number and irrational number always rational?

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


Is the product of a nonzero rational number and an irrational number rational or irrational?

It is always irrational.


What is the product of one irrational number and one rational number?

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


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

Not if the rational number is zero. In all other cases, the product is irrational.


Why the product of nonzero rational number and a rational number is an 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)


What does a rational number times an irrational number equal?

The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.


Is the product of a rational and irrational number always irrational?

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


Can you multiply an irrational number by a rational number and the answer is rational?

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


Is the product of two rational number irrational or rational?

It is always rational.