Let us suppose that is a rational number. Then there are positive integers a and b such that , where a and b are co-prime, meaning their HCF is 1.
We can see that a and b share at least 3 as a common factor from (1) and (2). The fact that a and b are co-prime, on the other hand, contradicts this and indicates that our hypothesis is incorrect. Therefore, is an irrational number.
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