0
Zero is several sorts of numbers. It is actually both. "Real numbers", "Rational numbers", "Irrational Numbers", "integers", "trancendental numbers", "cardinal numbers" and so forth, all have their own definitions. These definitions define a SET of numbers. A single number can belong to several SETs.
Real numbers are numbers that can be written as an infinite decimal expansion. It includes numbers like fractions eg 1/7 and PI. Real numbers can also be split into algebraic and transcendental numbers but the definition is too complicated here. 0 is a member of this SET
Rational numbers work out to be the same but there is a slightly different definition. 0 is a member of this SET
Irrational numbers belong to the set of two dimensional numbers of the vector form a + b x i where i is the square root of -1. 0 = 0 + 0 x i so zero is also a member of this SET
Integers are the set of normal counting numbers both positive, negative and 0.
I have not included any more here because they are a part of number theory and not part of a discussion on logic (SETs).
No, it is a rational number.
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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 is the product of a non - zero rational number and an irrational number is irrational?
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.
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)
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 is the product of one irrational number and one rational number?
Provided that the rational number is not 0, the product is 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 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.
Is the product of a rational and irrational number always irrational?
No, but the only exception is if the rational number is zero.
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 the rational zero test be used to find irrational roots as well as rational roots?
Rational zero test cannot be used to find irrational roots as well as rational roots.
Why is the product of a non - zero rational number and an irrational number is irrational?
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.
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 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 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 is the product of one irrational number and one rational number?
Provided that the rational number is not 0, the product is irrational.
