The product of two rational number is always rational.
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
Such a product is always irrational - unless the rational number happens to be zero.
The question is nonsense because the product of two rational numbers is never irrational.
No, they are complementary sets. No rational number is irrational and no irrational number is rational.Irrational means not rational.
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!
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.
No. If it was a rational number, then it wouldn't be an irrational number.
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.
Provided that the rational number is not 0, the product is irrational.
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.
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)
It is always 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.
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.).
No. Real numbers are divided into two DISJOINT (non-overlapping) sets: rational numbers and irrational numbers. A rational number cannot be irrational, and an irrational number cannot be rational.
No.A rational times an irrational is never rational. It is always irrational.
Not if the rational number is zero. In all other cases, the product is irrational.
The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.
The product will be irrational.
If you multiply a rational and an irrational number, the result will be irrational.
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.
Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).
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.
It will be irrational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.