Question

I have to prove that √3 is an irrational no by long division method.How to do the same in easier way.

Answer 1

√3 can be represented as ab, where a and b have no common factors.

So 3=a²b² and 3*b²=a². Now a² must be divisible by 3, but then so must a (fundamental theorem of arithmetic). So we have 3b²=(3k)² and 3b²=9k² or even b²=3k² and now we have a contradiction.