Why do you need rational and irrational numbers '?

Answer 1

Because rational numbers are not closed under fractional exponents. For example, the square root of 2 is not a rational number. Nor is a cube root of 2, or a square root of 5, etc.

And in case you are wondering about the relevance of the square root of 2, it is the length of the diagonal of a unit square - and so it is the longest length that can fit inside a 1x1 square.

Answer 2

to do fractions, to multiply divisions