Well, the radical sign is usually used to take roots of numbers.  without an index, it is understood to be a squareroot, otherwise it is the nth roo of the number, with n being the index.

rational numbers are numbers which can be xpressed in the form of a/b.  simply saying, it can be expressed as a fraction.  obviously, irrational numbers cant be expressed through fractions.  examples of rational numbers are 20, 0.10, 1/9, 4.5, and 100.  example of irrational numbers are squareroot of 2, pi, squareroot of 3, cuberoot of 5, 10th root of 9

hope this helps :)