# Prove that is an irrational number.

To prove is irrational, let's assume it is a rational number.

Hence, can be written is form of Hence, are co-prime and   Squaring both sides _____(a) this means is divided by By theorem = If is a prime number of divides then also divides So we can say [hence k is integer] _____(b)

Putting the value of (b) in (a)   Here we could also say that is divided by . By the theorem stated above, b should also be divisible by  hence a & b both are divisible by but as we know a&b are co-prime (hence they can't have a co-factor ) Hence by contradiction, is an irrational number.

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