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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∈

( 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