Question

prove that 3+2√5 is a irrational

Answer 1

let 3 +2√5 be irrational number.

noe answer is on pic.

Answer 2

Assum that 3+2 root5 is rational

3+2 root5 =p/q ( p, q are integers without having a common factor)

3+2 root 5=p/q

2+root5 =p/q - 3

Root 5 =p-3q/2q

P, q are integer

P-3q/2q is rational

But we know that root 5 is irrational

This is a contradiction

Our assumption is wrong

Therefore, 3+2 root5 is irrational

Hope this is helpfull.....