query: Prove square root of 3 is irrational
positive_passages.docid: 1383
positive_passages.text: How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
negative_passages.docid: 127830
negative_passages.text: proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
negative_passages.docid: 96204
negative_passages.text: Irrational number $\sqrt2$ proof
negative_passages.docid: 7463
negative_passages.text: Square root of a square
negative_passages.docid: 10008
negative_passages.text: Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
negative_passages.docid: 68838
negative_passages.text: Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
negative_passages.docid: 101162
negative_passages.text: Square root of $2$ is irrational
negative_passages.docid: 37915
negative_passages.text: $\sqrt{2}$ is irrational proof using well-Ordering Property
negative_passages.docid: 114793
negative_passages.text: Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational
negative_passages.docid: 30478
negative_passages.text: How to prove that a number is irrational
negative_passages.docid: 125267
negative_passages.text: Prove that $2^{1/2}$ is irrational
negative_passages.docid: 39021
negative_passages.text: Proving that $\sqrt{2}+\sqrt{3}$ is irrational
negative_passages.docid: 77081
negative_passages.text: Proving square root of a square is the same as absolute value
negative_passages.docid: 143733
negative_passages.text: Is this proof that $\sqrt 2$ is irrational correct?
negative_passages.docid: 56802
negative_passages.text: Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
negative_passages.docid: 131634
negative_passages.text: Prove the irrationality of $0.235711131719...$
negative_passages.docid: 129433
negative_passages.text: $\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$ is Irrational