query: Prove or disprove that the sum of two irrational numbers is irrational
positive_passages.docid: 26394
positive_passages.text: Is the sum and difference of two irrationals always irrational?
negative_passages.docid: 99311
negative_passages.text: Prove $2^{1/3} + 2^{2/3}$ is irrational
negative_passages.docid: 24706
negative_passages.text: Is there a rational number between any two irrationals?
negative_passages.docid: 129433
negative_passages.text: $\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$ is Irrational
negative_passages.docid: 83145
negative_passages.text: Sum of rational numbers
negative_passages.docid: 1383
negative_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: 158066
negative_passages.text: Prove $2^{1/3}$ is irrational.
negative_passages.docid: 30622
negative_passages.text: Proving $\sqrt 3$ is irrational.
negative_passages.docid: 4381
negative_passages.text: Proof that the set of irrational numbers is dense in reals
negative_passages.docid: 70315
negative_passages.text: Process to show that $\sqrt 2+\sqrt[3] 3$ is irrational
negative_passages.docid: 138446
negative_passages.text: Proving that there exists an irrational number in between any given real numbers
negative_passages.docid: 120906
negative_passages.text: Is there a proof that $\pi \times e$ is irrational?
negative_passages.docid: 4946
negative_passages.text: Non-existence of irrational numbers?
negative_passages.docid: 44476
negative_passages.text: Can we ever get an irrational number by dividing two rational numbers?
negative_passages.docid: 126074
negative_passages.text: Proof of the irrationality of $\sqrt{3}$ - logic question
negative_passages.docid: 10882
negative_passages.text: irrationality of $\sqrt{2}^{\sqrt{2}}$.
negative_passages.docid: 81428
negative_passages.text: Why does proof by contradiction not work on Rational numbers but only on Irrational numbers?