Xelios,
Pi is not the quotient of two integers; it's not 22/7 or any other quotient of integers. A number that is not the quotient of integers is called an irrational number. So pi is irrational. But a number that is irrational and is not the root of any algebraic equation is called transcendental. Pi is transcendental.
There's a simple proof, due to the Greeks - Euclid, I think - that the square root of 2 is irrational. You might want to look that up.