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For ex:- √2
=let us assume that √2 is an rational number.
=let a and b are two co-primes.

√2 is rational so

squaring on both sides
so, 2b²=a²
so, 2 divides a² and 2
divides a
let, a = 2c

so, b²=(2c²)/2
so, 2 divides b² and 2
divides b

but according to the fact co-primes do not have the same factor i.e.., a and b have the factor 2

so, this contradicts our fact that √2 is rational.

so that √2is an irrational number
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