query: Irrationality of $r\sqrt{5}$ for rational number $r$?
positive_passages.docid: 151876
positive_passages.text: Is irrational times rational always irrational?
negative_passages.docid: 114793
negative_passages.text: Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational
negative_passages.docid: 118374
negative_passages.text: Is there a proof that $\pi$ is an irrational number?
negative_passages.docid: 84558
negative_passages.text: Prove that the square root of a positive integer is either an integer or irrational
negative_passages.docid: 55077
negative_passages.text: prove that $2\sqrt5 +\sqrt{11}$ is irrational
negative_passages.docid: 92226
negative_passages.text: Prove $\sqrt6$ is irrational
negative_passages.docid: 128298
negative_passages.text: Irrationality of sum of two logarithms: $\log_2 5 +\log_3 5$
negative_passages.docid: 30622
negative_passages.text: Proving $\sqrt 3$ is irrational.
negative_passages.docid: 23752
negative_passages.text: Proving Irrationality
negative_passages.docid: 87596
negative_passages.text: Is $\sum_{p}\frac{1}{p^{2}}$ irrational?
negative_passages.docid: 104548
negative_passages.text: Geometric proof for irrationality of $\pi$
negative_passages.docid: 7801
negative_passages.text: Can you raise a number to an irrational exponent?
negative_passages.docid: 40009
negative_passages.text: Show that $e^{\sqrt 2}$ is irrational
negative_passages.docid: 158730
negative_passages.text: Is $\ln(\ln(n))$ irrational for any integer $n>1$?
negative_passages.docid: 30478
negative_passages.text: How to prove that a number is irrational
negative_passages.docid: 81957
negative_passages.text: How many roots have a complex number with irrational exponent?
negative_passages.docid: 19676
negative_passages.text: Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?