Can you add two irrational numbers to get an irrational number?

Yes.

An example:

1 + 2^(0.5) is an irrational number,

1 -(2^(0.5)) is also a irrational number.

(1 + 2^(0.5)) + (1- 2^(0.5)) = 2

2 is a rational number.

Therefore the sum of two Irrational Numbers can equal a rational number.

But this is not the question. Can you add two irrational numbers to get another irrational number. Yes. Almost all additions of two irrational numbers result in another irrational number. For instance pi (3.141...) and e (2.718...) are both irrational, and so is their sum. In some sense you have to work quite hard to make the sum not irrational (i.e. rational) because the two decimal expansions have to conspire together either to cancel out or to give a repeating decimal.

Actually, pi+e may or may not be irrational. This hasn't been proved either way. See: http://en.wikipedia.org/wiki/Irrational_number (under "Open Questions")
Yes. For example, pi + (-pi) = 0.
any number that is a non-terminating decimal is called an irrational number.