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Can the product of any two irrational numbers be a rational number?
Wiki User
∙ 12y ago
Yes. For example, if you multiply the square root of 2 (an irrational number) by itself, the answer is 2 (a rational number). The golden ratio (Phi, approx. 1.618) multiplied by (1/Phi) (both Irrational Numbers) equals 1 (rational).
However, this is not necessarily true for all irrational numbers.
Wiki User
∙ 12y ago
Anonymous
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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.).
The rational numbers are a subset of the irrational numbers?
No, they are complementary sets. No rational number is irrational and no irrational number is rational.Irrational means not rational.
Is the product of three rational numbers rational or irrational?
A rational number in essence is any number that can be expressed as a fraction of integers (i.e. repeating decimal). Taking the product of any number of rational numbers will always yield another rational number.
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 121 an irrational number?
NO this number is way far from irrational, first of all let's classify this number, it's an integer, whole number, rational, even a perfect square. This number has two numbers that are not irrational. one example is 11, 11 those numbers are rational so the product can't be irrational.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
Why is the product of two rational number irrational?
The question is nonsense because the product of two rational numbers is never 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.
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.
Can irrational numbers be rational numbers?
No. If it was a rational number, then it wouldn't be an irrational number.
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!
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.).
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 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.
Are rational numbers is an irrational numbers?
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
Is there any number x such that x² is an irrational number and x's is a rational number?
no x² is the product of 2 rational numbers in this case the same 2 numbers x and x The product of two rational numbers is always rational.
