Yes. Any irrational number can be divided by itself to produce 1, which is a rational number.
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Irrational.
No. sqrt(2)/pi is not rational.
No. An irrational number is one that is not a rational number. A rational number is once that equals one integer divided by another. So an irrational number cannot be represented by one integer divided by another integer, so it cannot be an integer!
Yes it will be. The set of real numbers can be divided into two distinct sets: rational and irrational. So if it is not rational, then it is irrational.
It is irrational - unless the divisor is 0 in which case the division is not defined.