Question

Prove that 2+3root5 is irrational

Answer 1

let us consider 2+3root5 is rational
then it can be represented in the form p/q
so,
    2+3root5 = p/q
 or root5 = (p-2q)/3p

but p and q are rational and root5 is not.
so 2+3root5 is irrational