query: Direct Irrationality Proof for $\sqrt{3}$ and $\sqrt{6}$
positive_passages.docid: 6275
positive_passages.text: How can you prove that the square root of two is irrational?
negative_passages.docid: 142000
negative_passages.text: Prove that there is an irrational number and a rational number between any two distinct real numbers
negative_passages.docid: 67605
negative_passages.text: Different proof that $\sqrt{2}$ is irrational
negative_passages.docid: 75639
negative_passages.text: Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
negative_passages.docid: 32
negative_passages.text: Is $n^{th}$ root of $2$ an irrational number?
negative_passages.docid: 129521
negative_passages.text: Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
negative_passages.docid: 89716
negative_passages.text: Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
negative_passages.docid: 77129
negative_passages.text: Density of irrationals
negative_passages.docid: 63804
negative_passages.text: Proof that every repeating decimal is rational
negative_passages.docid: 68456
negative_passages.text: Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
negative_passages.docid: 88429
negative_passages.text: Prove $\sqrt{2} + \sqrt{5}$ is irrational
negative_passages.docid: 64885
negative_passages.text: Irrational and rational sequence proof
negative_passages.docid: 15210
negative_passages.text: Group of order 6 proof
negative_passages.docid: 128298
negative_passages.text: Irrationality of sum of two logarithms: $\log_2 5 +\log_3 5$
negative_passages.docid: 118374
negative_passages.text: Is there a proof that $\pi$ is an irrational number?
negative_passages.docid: 131634
negative_passages.text: Prove the irrationality of $0.235711131719...$
negative_passages.docid: 124641
negative_passages.text: Prove that $5^{1/3}+7^{1/2}$ is irrational