# 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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