Let n>2. Where n is integer show that sqrt(n!) is irrational. 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.