I was reading another post on here (unfortunately, I couldn't comment on the post due to my low reputation), one poser wrote "that a degree 3 extension of a field does not admit new square elements". I am just confused at what this statement means and why this is.
To give contexts, I want to show that an irreducible polynomial $x^3 + px + q$ over a finite field $K$ characteristic not 2 or 3, then $-4p^3 - 27q^2$ is square in $K$. I know that $-4p^3 - 27q^2$ is the discriminant of the said polynomial and that the discriminant is a square in the splitting field, which has degree 3. Now, I just want to conclude that it is also a square in $K$.