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 :)