# Find the degree of QQ(sqrt 2) over QQ

Seettiffrourfk6 2022-10-15 Answered
Find the degree of $\mathbb{Q}\left(\sqrt{2}\right)$ over $\mathbb{Q}$
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## Answers (1)

silenthunter440
Answered 2022-10-16 Author has 19 answers
${x}^{4}-4=\left({x}^{2}-2\right)\left({x}^{2}+2\right)$ is not irreducible. The minimal polynomial is ${x}^{2}-2$ so the degree is 2. The minimal polynomial is unique up to a constant factor.
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