Question

prove that 5 + 7 root 3 is rational

Answer 1

Let it be rational no so it is in the form of p/q.

=>5+7√3=p/q

=>7√3=p/q-5

=>√3=1/7(p/q-5)

=>Since, LHS is irrational and RHS is rational so our contradiction is wrong hence 5+7√3 is irrational.