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Is a rational number divided by an irrational number always irrational?
Wiki User
∙ 14y ago
No. If we let x be irrational, then 0/x = 0 is a counterexample.
However, if we consider nonzero rational numbers, then our conjecture is true. We shall prove this by contradiction.
Suppose we have nonzero rational numbers x and y, and an irrational number z, such that x/z = y. Since z is not equal to 0, x = yz. Since y is not equal to 0, x/y = z. Since x/y is a quotient of rational numbers, x/y is rational. Therefore, z is rational, contradicting our assumption that z was irrational. QED.
Wiki User
∙ 14y ago
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Is the product of a nonzero rational number and an irrational number rational or irrational?
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 4 divided by 9 an irrational number?
0.4444
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 an irrational number divided by an irrational number equals an irrational number?
Yes, an irrational number divided by an irrational number will usually be an irrational number, but not always. For example, pi / (3pi) is 1/3, which is a rational number, but pi/e is an irrational number.
Is an irrational number divided by an irrational number always a rational?
No. sqrt(2)/pi is not rational.
When an irrational number is divided by a rational number is the quotient rational or irrational?
Irrational.
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 irrational number always rational?
No.A rational times an irrational is never rational. It is always irrational.
Can An irrational number divided by an irrational number equals a rational number?
Yes. Any irrational number can be divided by itself to produce 1, which is a rational number.
Is the sum of a rational and irrational number rational or irrational?
It is always irrational.
Is the product of a nonzero rational number and an irrational number rational or irrational?
It is always irrational.
When you multiply an irrational number by a rational number will the answer always be irrational rational or both?
It will be 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
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 4 divided by 9 an irrational number?
0.4444
