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Q: Is the product of a rational number and a rational number a rational number?

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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.

It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.

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

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

Negative. Only like x like = positive

Related questions

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

The product of two rational numbers is always a rational number.

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

If the multiplicative inverse exists then, by definition, the product is 1 which is rational.

The product will also be a rational number

another rational number

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

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)

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.

It is a rational number.

It is a rational number.

It is always rational.

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