Why must n be divisible by 2 if n^2 is divisible by 2? Also, does this apply to irrational numbers and variables? I.e. if n^2 is divisible by p then n must be divisible by p.

View attachment 37694
Why must n be divisible by 2 if n^2 is divisible by 2? Also, does this apply to irrational numbers and variables? I.e. if n^2 is divisible by p then n must be divisible by p.

if n^2 is divisible by 2, that means n^2 is an even number. since (odd number)^2 = always odd and (even number)^2 = always even, that means n is an even number like n^2 and hence also divisible by 2.

irrational numbers are neither odd nor even because they aren't integers so we can't use that same logic i think

if n is div by 2, n=2p
hence n^2= 4p^2= 2(2p^2) which is divisible by two
Irrational numbers can't be divisible by two (or any integer for that matter)