Suppose n=ab, show that a^2<=n or b^2<=n.
Start with trichotomy: a < b, a = b, or a > b. It's pretty simple.
I'm fairly new to proofs, so can you please check if this is correct.
if a=b, n=a^2 or b^2=n
if a>b, a^2>ab, a^2>n
if b>a, b^2>ab, b^2>n
What you write is correct, though for the last two you should really use the opposite variable (and reverse signs) because you're trying to show that something's smaller, not bigger.
Try multiplying a > b by b instead of by a.
so it should be like this then:
if a>b, ba>b^2, n>b^2
if b>a, ab>a^2, n>a^2
Separate names with a comma.