To express certain numbers that can't be expressed as a rational number - i.e., that you can't write as a fraction, with integers in the numerator and the denominator.
It can be but need not be.
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, because if need be it can be expressed as a fraction whereas irrational numbers can't be expressed as fractions.
No. For example, -root(2) + root(2) is zero, which is rational.Note that MOST calculations involving irrational numbers give you an irrational number, but there are a few exceptions.
An irrational number.
If you want to use a rational number for a mathematical operation, it will be necessary to estimate it for a numerical outcome. Irrational numbers can't be written out exactly.
The sum of a rational and irrational number must be an irrational number.
No. The sum of an irrational number and any other [real] number is irrational.
No number can be both rational and irrational. And, at the level that you must be for you to need to ask that question, a number must be either rational or irrational (ie not neither). 0.555555 is rational.
rational * irrational = irrational.
No, 3.56 is not an irrational number. 3.56 is rational.
-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.