query: What does $\mathbb{Q}(\sqrt{2},\sqrt{3})$ mean?
positive_passages.docid: 148876
positive_passages.text: What is the meaning of $\mathbf{Q}(\sqrt{2},\sqrt{3})$
negative_passages.docid: 21457
negative_passages.text: Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
negative_passages.docid: 11564
negative_passages.text: $\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
negative_passages.docid: 92517
negative_passages.text: Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
negative_passages.docid: 87682
negative_passages.text: Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
negative_passages.docid: 63478
negative_passages.text: Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
negative_passages.docid: 30404
negative_passages.text: Is $\mathbb{Z}/3\otimes \mathbb{Z}[1/2]=\mathbb{Z}/3$?
negative_passages.docid: 108550
negative_passages.text: Elements of $\mathbb Q(2^{1/3})$
negative_passages.docid: 109952
negative_passages.text: Find the minimal polynomial of $\sqrt2 + \sqrt3 $ over $\mathbb Q$
negative_passages.docid: 76685
negative_passages.text: Determine $\text{Aut}(S)$ where $S = \mathbb{Q}[x]/(x^2)$
negative_passages.docid: 46831
negative_passages.text: Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
negative_passages.docid: 138193
negative_passages.text: Why is $\sqrt {12} = 2 \sqrt 3$?
negative_passages.docid: 50172
negative_passages.text: Show that $\mathbb{Q}(\sqrt{2})$ is the smallest subfield of $\mathbb{C}$ that contains $\sqrt{2}$
negative_passages.docid: 34906
negative_passages.text: Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.
negative_passages.docid: 126427
negative_passages.text: Proving $\sqrt{2}+\sqrt[3]{3}$ is algebraic.
negative_passages.docid: 50668
negative_passages.text: Show that $\mathbb{Q}(\sqrt2, \sqrt[3]2)$ is a primitive field extension of $\mathbb{Q}$.
negative_passages.docid: 16163
negative_passages.text: Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.