Question

Please help me with the question :
show that Q[x]/(x^2-2) is not isomorphic with Q[x]/(x^2-3)

Answer 1

hmm i think i remember this gimmick but it was with \(\mathbb{Q}(\sqrt2)\) and \(\mathbb{Q}(\sqrt3)\)

Answer 2

since they are the same thing, it must be the same
the hint is to show that if you had such an isomorphims, since \(\phi(1)=1\) it must be the case that \(\phi(\sqrt2)=\sqrt2\) but \(\sqrt 2\notin \mathbb{Q}(\sqrt3)\)

Answer 3

you are right
it is similar , but this one is little bit more trickier!