Question

Prove that under root 2 is irrational?

Answer 1

u can do this by doing long division or see this
let assume √2 be rational
√2=p/q ( let p and q are having no common factor that is one is their factor and q≠0
2=p²/q²
p²=2q²
p² is an even integer (if p is not even integer then p=2m+1,m∈ Z)
                                  ( p²=(2m+1)² =4m²+4m+1,which is odd)
p=2m (where m is a integer)
p²=4m²
2q²=4m²
q²=2m²
q² is a even integer
q is a even intager
now in this both q and p r having common factor other than 1 that is 2
so, our thinking is wrong of √2 as rational
∴√2 is an irrational