2^(1/n) is irrational for n > 2

Theorem: $2^{\frac{1}{n}}$ is irrational for $n > 2$

Let us assume that

$2^{\frac{1}{n}} = \frac{p}{q}$

$\implies 2 = \frac{p^n}{q^n}$

$\implies 2q^n= p^n$

$\implies q^n+q^n=p^n$ which by fermat’s last theorem is impossible 🙂

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