(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] extension fields

1. The problem statement, all variables and given/known data

Prove that x^2-3 is irreducible over [tex]\mathbb{Q}(\sqrt{2})[/tex].

EDIT: it should be [tex]\mathbb{Q}(\sqrt[3]{2})[/tex]

2. Relevant equations

3. The attempt at a solution

So, we want to show that [itex]\sqrt{3}[/itex] and [itex]-\sqrt{3}[/itex] are not expressible as [itex]a +b(\sqrt[3]{2})^2 +c\sqrt[3]{2}[/itex]. We could take the sixth power of both sides, but then the equation would be just messy. What else can we do?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Extension fields

**Physics Forums | Science Articles, Homework Help, Discussion**