query: How to show $\sqrt{3} + \sqrt{2}$ is algebraic?
positive_passages.docid: 21972
positive_passages.text: How to show that $\sqrt{2}+\sqrt{3}$ is algebraic?
negative_passages.docid: 148876
negative_passages.text: What is the meaning of $\mathbf{Q}(\sqrt{2},\sqrt{3})$
negative_passages.docid: 70315
negative_passages.text: Process to show that $\sqrt 2+\sqrt[3] 3$ is irrational
negative_passages.docid: 122083
negative_passages.text: Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
negative_passages.docid: 56420
negative_passages.text: Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
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: 7201
negative_passages.text: Prove that $x_1^2+x_2^2+x_3^2=1$ yields $ \sum_{i=1}^{3}\frac{x_i}{1+x_i^2} \le \frac{3\sqrt{3}}{4} $
negative_passages.docid: 90276
negative_passages.text: Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
negative_passages.docid: 35216
negative_passages.text: Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
negative_passages.docid: 99516
negative_passages.text: Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
negative_passages.docid: 32760
negative_passages.text: Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
negative_passages.docid: 109953
negative_passages.text: How to prove that $\sqrt 3$ is an irrational number?
negative_passages.docid: 44440
negative_passages.text: Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
negative_passages.docid: 62485
negative_passages.text: How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
negative_passages.docid: 37529
negative_passages.text: If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
negative_passages.docid: 126074
negative_passages.text: Proof of the irrationality of $\sqrt{3}$ - logic question
negative_passages.docid: 67666
negative_passages.text: show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$