That ain't necessarily true in all cases. For example, square root of 2 Times Square root of 2 is equal to two, which is RATIONAL.
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 irrational.
An irrational number.
It is an irrational number.
It is always irrational.
Yes.
Yes, always.
The product will be irrational.
Yes, always.
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.
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The quotient of a nonzero rational number and an irrational number is always an irrational number. This is because dividing a rational number (which can be expressed as a fraction of integers) by an irrational number cannot result in a fraction that can be simplified to a rational form. Therefore, the result remains outside the realm of rational numbers.