Irrational Numbers

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)

The product will be irrational.

It is an irrational number.

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

An irrational number.

Suppose a is rational (and non-zero) and x is irrational. Suppose ax is rational;write ax = b where b is rational.Then x = b/a, and x would be rational, contradiction.

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.

The question cannot be answered because it is based on a false premise.The product of a (not an!) rational number and an irrational number need not be irrational. For eample, the product ofthe rational number, 0, and the irrational number, pi, is 0. The product is rational, not 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.

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

If you multiply a rational and an irrational number, the result will be irrational.

It means that: a) The number is irragional, and b) the number is not zero. Since zero is rational, it isn't irrational, so saying that it is nonzero is really superfluous.

Not necessarily. 0 times any irrational number is 0 - which is rational.

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

No. If the rational number is not zero, then such a product is irrational.

It is always rational.

Yes, as long as the two nonzero numbers are themselves rational. (Since a rational number is any number that can be expressed as the quotient of two rational numbers, or any number that can be written as a fraction using only rational numbers.) If one of the nonzero numbers is not rational, the quotient will most likely be irrational.

The product of two rational number is always rational.

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