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.
It is irrational.
The product will be irrational.
It is an irrational number.
The product of an irrational number and a rational number, both nonzero, is always irrational
An irrational number.
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.
Provided that the rational number is not 0, the product is 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.
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.
If you multiply a rational and an irrational number, the result will be 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!
Yes, as long as the two nonzero numbers are themselves rational. (Since a rational number is any number that can be expressed as the quotient of two rational numbers, or any number that can be written as a fraction using only rational numbers.) If one of the nonzero numbers is not rational, the quotient will most likely be irrational.
Not necessarily. 0 times any irrational number is 0 - which is rational.
No, but the only exception is if the rational number is zero.
Yes, except in the degenerate case where the rational number is 0, in which case the product is also 0, a rational result.
No, it cannot. The product of a rational and irrational is always irrational. And half a number is equivalent to multiplication by 0.5
It is a rational number.
It means that: a) The number is irragional, and b) the number is not zero. Since zero is rational, it isn't irrational, so saying that it is nonzero is really superfluous.
Yes, it is possible only if an irrational number is multiplied with 0.