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Why is the product of a non - zero rational number and an irrational number is irrational?
Wiki User
∙ 8y ago
Let q be a non-zero rational and x be an irrational number.Suppose q*x = p where p is rational.
Then x = p/q.
Then, since the set of rational numbers is closed under division (by non-zero numbers), p/q is rational.
But that means that x is rational, which contradicts x being irrational.
Therefore the supposition that q*x is rational must be false
ie the product of a non-zero rational and an irrational cannot be rational.
Wiki User
∙ 7y ago
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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.
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 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 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.
Is the product of a rational and irrational number always irrational?
No, but the only exception is if the rational number is zero.
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".
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 it true product of a non zero rational number and irrational number is rational number?
It is always FALSE.
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 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 it always sometimes or never true that the product of a non zero rational number and an irrational number is irrational?
It is always true.
