Are We Being Totally Irrational?

In 8th grade math class we've been playing around with numbers.
Perfect squares.
Cubes.
Square roots.
Cube roots.
We've been ordering them and plotting them on number lines.
Today we sorted them into two groups,
And through close analysis discovered something else about these numbers we had been working with!

Ask your student...
1.  What is an irrational number?
2.  What is a rational number?
3.  How can you tell the difference between an irrational and rational number?
4.  Can a number be both irrational and rational?
5.  How did you learn the differences between irrational and rational numbers?
6.  What is the hardest thing to remember?