Question

Prove that 2+3root5 is irrational number

Answer 1

Answer:

let us assume that 2+3√5 is rational

→ 2+3√5=a/b (where 'a' and 'b' are two co-prims where b ≠0)

→2+3√5=a/b

3√5=a/b -2

3√5= a-2b/b

√5=a-2b/3b

→since, in RHS √5 is equal to LHS but a irrational number cannot be equal to rational number

→this contradiction has arrisen because of our incorrect assumption

→so we conclude that 2+3√5is. irrational number