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Why is the productof a non zero rational number and an irrational number is irrational?
Wiki User
∙ 9y ago
Let A be a non-zero rational number and B be an irrational number and let A*B = C.Suppose their product C, is rational.
Then, dividing both sides of the equation by A gives B = A/C.
Now, since A and C are both rational, A/C must be rational.
Therefore you have B (irrational) = A/C (irrational).
Clearly, this is impossible and therefore the supposition must be wrong. That is to say, A*B cannot be ration or, it must be irrational.
Wiki User
∙ 7y ago
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What is the result of an irrational number times an rational number?
Unless the rational number is zero, the answer is irrational.
Is the product of a rational and irrational number always irrational?
No, but the only exception is if the rational number is zero.
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 product of a rational and irrational number?
It is usually irrational but it can be rational if the ration number in the pair is zero. So the correct answer is "either".
What happens when a rational number is divided by an irrational number?
When a rational numbers is divided by an irrational number, the answer is irrational for every non-zero rational number.
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.
What is the result of an irrational number times an rational number?
Unless the rational number is zero, the answer 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)
Is the product of a rational and irrational number always irrational?
No, but the only exception is if the rational number is zero.
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.
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.
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 product of one irrational number and one rational number?
Provided that the rational number is not 0, the product is irrational.
What is the product of a rational and irrational number?
It is usually irrational but it can be rational if the ration number in the pair is zero. So the correct answer is "either".
Is 3pi an irrational number?
Yes. Any time you multiply a rational number by an irrational number, you get an irrational number - unless the rational number is zero.
Does multiplying rational and irrational numbers lead to an irrational number result?
Yes, but only if the rational number is non-zero.
