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

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1. misty1212

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

2. misty1212

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 $$\sqrt 2\notin \mathbb{Q}(\sqrt3)$$

3. anonymous

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