no
Integers are rational. In the set of real numbers, every number is either rational or irrational; a number can't be both or neither.
no
You can not add irrational numbers. You can round off irrational numbers and then add them but in the process of rounding off the numbers, you make them rational. Then the sum becomes rational.
3/8 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
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.
The square roots of three are examples of irrational numbers.
No, it is rational.
No, it is rational.
The sum of the three can be rational or irrational.
The formal definition of rational numbers is: Any fractionwith whole numbers on top and bottom.
Numbers can be ordinal, cardinal or imaginary. They could also be fractional, decimal, rational or irrational.
There cannot be a proof since your assertion is not necessarily true. sqrt(2)*sqrt(3) = sqrt(6). All three are irrational numbers.