What does $\mathbb{Q}(\sqrt{2})$ mean? Is it $\{ a+b\sqrt{2} \mid a, b \in \mathbb{Q} \}$ ?
2026-04-03 11:19:24.1775215164
notation in abstract algebra: $\mathbb{Q}(\sqrt{2})$
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Yes. Formally, $\mathbb{Q}(a)$ means “the smallest field containing $a$ and $\mathbb{Q}$". It turns out that the smallest field containing both $\mathbb{Q}$ and $\sqrt{2}$ is precisely the field you wrote.