Let n>2. Where n is integer show that sqrt(n!) is irrational.(adsbygoogle = window.adsbygoogle || []).push({});

I am supposed to use the Chebyshev theorem that for n>2. There is a prime p such that n<p<2n.

So far I am up to inductive hypothesis. Assume it holds for k then show it holds for k+1.

Well if k! is irrational==> k!= 2^(e_2)***p^(e_n)

then there is one power of prime which is odd. Using number theory. But don't know any ideas how to go from there.

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# Show that sqrt(n!) is irrational

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