query: Finding out if a number is rational or irrational.
positive_passages.docid: 23752
positive_passages.text: Proving Irrationality
negative_passages.docid: 4946
negative_passages.text: Non-existence of irrational numbers?
negative_passages.docid: 28347
negative_passages.text: Prove that $\sqrt 2 + \sqrt 3$ is irrational
negative_passages.docid: 48975
negative_passages.text: Transcendental numbers and irrationality measure
negative_passages.docid: 78287
negative_passages.text: Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
negative_passages.docid: 96204
negative_passages.text: Irrational number $\sqrt2$ proof
negative_passages.docid: 11069
negative_passages.text: Deciding whether $2^{\sqrt2}$ is irrational/transcendental
negative_passages.docid: 151325
negative_passages.text: (How to/Can I) show irrational numbers?
negative_passages.docid: 22408
negative_passages.text: Jutifying: irrational + rational = irrational
negative_passages.docid: 92226
negative_passages.text: Prove $\sqrt6$ is irrational
negative_passages.docid: 83145
negative_passages.text: Sum of rational numbers
negative_passages.docid: 152512
negative_passages.text: What is the ratio of rational to irrational real numbers?
negative_passages.docid: 19076
negative_passages.text: If a.b.c,d are rationals and x is irrational number, then prove that $\frac{ax+b}{cx+d}$ is usually a irrational number. When do exceptions occur?
negative_passages.docid: 50555
negative_passages.text: Approximation of real number to the power of irrational
negative_passages.docid: 140949
negative_passages.text: Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
negative_passages.docid: 151876
negative_passages.text: Is irrational times rational always irrational?
negative_passages.docid: 56877
negative_passages.text: Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.