• Is there a purely algebraic way to distinguish between the splitting fields of $x^2+2$ and $x2−2$?x^2−2$? The field$Q(\sqrt 2)$can be ordered while the field$Q(i\sqrt 2)$can not since -1 is a sum of squares. 1 One of your questions does have a positive answer. • Is there a purely algebraic way to distinguish between the splitting fields of$x^2+2$and$x2−2$? The field$Q(\sqrt 2)$can be ordered while the field$Q(i\sqrt 2)\$ can not since -1 is a sum of squares.