Find the degree of $\mathbb{Q}(\sqrt{2})$ over $\mathbb{Q}$

Seettiffrourfk6
2022-10-15
Answered

Find the degree of $\mathbb{Q}(\sqrt{2})$ over $\mathbb{Q}$

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silenthunter440

Answered 2022-10-16
Author has **19** answers

${x}^{4}-4=({x}^{2}-2)({x}^{2}+2)$ 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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