Irrational Numbers

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

###### Wiki User

It is always irrational.

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## Related Questions

### 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)

### 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

### Why the product of nonzero rational number and an irrational number is an irrational?

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.

### 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 rational or irrational?

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

### Why is the product of a rational number and an irrational number irrational?

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!

### 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.

### 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 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 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.

### 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.

### What is the classification of the product of a rational and an irrational number?

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

### What does nonzero irrational number mean?

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.

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

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

### Does a rational number times an irrational number equal a rational number?

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

### Is the quotient of two nonzero numbers always a rational number?

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.

### Is the product of two rational numbers irrational?

The product of two rational number is always rational.

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