#1**+3 **

Let us suppose that there exists integers a, b such that

√2 = a / b where a/b is reduced to lowest terms [a and b have no factors in common ]

So

b√2 = a square both sides

2b^2 = a^2

But a^2 must be even......so ......"a" must be even......

Then a = 2m ....so a^2 = 4m...so......

2b^2 = (2m)^2

2b^2 = 4m^2 divide both sides by 2

b^2 = 2m^2 then b must also be even

But....we assumed that a, b had no factors in common.....so.....they can't both be even

So....our aqssumption that

√2 = a / b must be false, since it leads to a false conclusion

CPhill Jan 7, 2019