Question

Proove that root 11 is an irrational number by contradiction method

Answer 1

Lets assume that √11 is rational

Therefore, √11 = P/Q     such that HCF (P,Q) =1 and Q not 0

Now, square on both sides,

11= P² / Q²

11 Q² = P²

Therefore, P² is divisible by 11 as well as P
Therefore, P = 5A  (where A is any integer

Hence √11 Q = 11 A

11 Q² = 121 A²

Q² = 11A²

Q² and Q are divisible by 11

Sice both P and Q are divisible by 11, HcF is not 1 , which is contradicting

And hence by contradiction method, √11 is an irrational number