Question

examine whether 3+√3 are rational or irrational

Answer 1

assume 3+√3 is rational

3+√3= a/b) where a and b have common factors other than 1) (they are not co prime)

cancelling common factors

3+√3=p/q(where p and q have common factors 1)

(they are co prime)

3+√3=p/q

√3=p/q-3

√3=(p-3q)/q

this is not possible because √3 is an irrational.

a rational can never be equal to an irrational

therefore 3+√3vis an irrational