Suppose sqrt(5) is rational
5 = (m/n)^2
5 = m^2/n^2 or m^2 = 5n^2
Since m^2 is a multiple of 5, m must also be a multiple of 5? - proof?
m = 5k for some int k
5n^2 = (5k)^2
5n^2 = 25k^2
n = 5k^2
n and m are both multiples of 5 this contradicts the assumption sqrt is irrational
end of work
My professor didnt like what i wrote in bold. I suppose she wanted me to write a proof out for this? how would I proceed? Is this broken up into cases?
ps. Im sorry I have so many topics in this area. Im trying my hardest to get by