I've wondered about this question for some time now
Read until you have something to write...Write until you have nothing to write...when you have nothing to write, read...read until you have something to write (http://handsonmath.blogspot.com/)
I am not sure the question has meaning. Those are mathematical terms, they represent sets. In the real world we have mostly measurements. They are accurate to some specified amount of decimal places. Even though we may be talking about a hypotenuse we say 1.41 miles not square root of 2 miles. Since measurements are terminating decimals the answer in my opinion is Rational.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.