query: Is there a way to show the sum of any different square root of prime numbers is irrational?
positive_passages.docid: 6869
positive_passages.text: The square roots of different primes are linearly independent over the field of rationals
negative_passages.docid: 83145
negative_passages.text: Sum of rational numbers
negative_passages.docid: 152172
negative_passages.text: Does there exist a positive irrational number $\alpha $, such that for any positive integer $n$ the number $\lfloor n\alpha \rfloor$ is not a prime?
negative_passages.docid: 28347
negative_passages.text: Prove that $\sqrt 2 + \sqrt 3$ is irrational
negative_passages.docid: 95111
negative_passages.text: Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
negative_passages.docid: 131731
negative_passages.text: Primes that can't be written as sum of two squares. Mod
negative_passages.docid: 7415
negative_passages.text: why only square root approach to check number is prime
negative_passages.docid: 138446
negative_passages.text: Proving that there exists an irrational number in between any given real numbers
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: 111094
negative_passages.text: Help with proving that $\pi$ 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: 78473
negative_passages.text: Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
negative_passages.docid: 22762
negative_passages.text: How can adding an infinite number of rationals yield an irrational number?
negative_passages.docid: 118374
negative_passages.text: Is there a proof that $\pi$ is an irrational number?
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: 46561
negative_passages.text: How can I prove that all rational numbers are either terminating decimal or repeating decimal numerals?
negative_passages.docid: 107105
negative_passages.text: Is an irrational number odd or even?