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=let us assume that √2 is an rational number.

=let a and b are two co-primes.

√2 is rational so

√2=a/b

√2b=a

squaring on both sides

so, 2b²=a²

b²=a²/2

so, 2 divides a² and 2

divides a

let, a = 2c

so, b²=(2c²)/2

b²=4c²/2

b²=2c²

b²/2=c²

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