Math and Arithmetic
Irrational Numbers

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

###### Wiki User

No.

A rational times an irrational is never rational. It is always irrational.

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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.

### 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 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.

### 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.

### 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 numbers irrational?

The product of two rational number is always 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.

### Can half of an irrational number be rational?

No, it cannot. The product of a rational and irrational is always irrational. And half a number is equivalent to multiplication by 0.5

### Is 10x 3.14 irrational?

The product of two rational numbers, as in this example, is always RATIONAL.However, if you mean 10 x pi, pi is irrational; the product of a rational and an irrational number is ALWAYS IRRATIONAL, except for the special case in which the rational number is zero.

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

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

### 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!

### 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.

### Does there exist an irrational number such that its square root is rational?

No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).

### Can you add irrational number and a rational to get a rational number?

If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.

### Is -9pie rational or irrational?

Irrational. If you multiply a rational number by an irrational number, you will always get an irrational number (except if the rational number happens to be zero).

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