query: How to show that $\sqrt{p\over p+1}$ is irrational?
positive_passages.docid: 156766
positive_passages.text: Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
negative_passages.docid: 2926
negative_passages.text: The contradiction method used to prove that the square root of a prime is irrational
negative_passages.docid: 143733
negative_passages.text: Is this proof that $\sqrt 2$ is irrational correct?
negative_passages.docid: 104548
negative_passages.text: Geometric proof for irrationality of $\pi$
negative_passages.docid: 64885
negative_passages.text: Irrational and rational sequence proof
negative_passages.docid: 139755
negative_passages.text: Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
negative_passages.docid: 67605
negative_passages.text: Different proof that $\sqrt{2}$ is irrational
negative_passages.docid: 20315
negative_passages.text: $\sqrt[31]{12} +\sqrt[12]{31}$ is irrational
negative_passages.docid: 147777
negative_passages.text: If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
negative_passages.docid: 34710
negative_passages.text: Cardinality of Irrational Numbers
negative_passages.docid: 39021
negative_passages.text: Proving that $\sqrt{2}+\sqrt{3}$ is irrational
negative_passages.docid: 30478
negative_passages.text: How to prove that a number is irrational
negative_passages.docid: 30411
negative_passages.text: The closure of the irrational numbers on $\mathbb{R}$
negative_passages.docid: 109953
negative_passages.text: How to prove that $\sqrt 3$ is an irrational number?
negative_passages.docid: 144244
negative_passages.text: Bound on difference between irrational square root and rational number
negative_passages.docid: 37642
negative_passages.text: Why is $\pi$ irrational if it is represented as $C/D$?
negative_passages.docid: 18360
negative_passages.text: Proof that the irrational numbers are uncountable