But is not unique. and both satisfy the equation .
Given any r which is an element of the positive rational numbers, the number root(r) is unique in the sense that, if x is a positive real number such that x^2 = r, then x = root(r).
I know that in order to prove uniqueness, one needs to show that if x^2 = r = y^2 where x and y are elements from the positive rationals, then x = y. But I am not sure how to go about doing this. Any help would be appreciated!