query: Is $\sqrt{2}+\sqrt{3}$ rational or irrational?
positive_passages.docid: 22800
positive_passages.text: Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
negative_passages.docid: 1190
negative_passages.text: Square Root of Rational Number $\frac{A}{B}$
negative_passages.docid: 40009
negative_passages.text: Show that $e^{\sqrt 2}$ is irrational
negative_passages.docid: 122226
negative_passages.text: Incorrect logic in popular proof of the irrationality of $\sqrt2$?
negative_passages.docid: 11069
negative_passages.text: Deciding whether $2^{\sqrt2}$ is irrational/transcendental
negative_passages.docid: 129521
negative_passages.text: Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
negative_passages.docid: 56802
negative_passages.text: Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
negative_passages.docid: 99835
negative_passages.text: Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
negative_passages.docid: 42444
negative_passages.text: Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$
negative_passages.docid: 67605
negative_passages.text: Different proof that $\sqrt{2}$ is irrational
negative_passages.docid: 99311
negative_passages.text: Prove $2^{1/3} + 2^{2/3}$ is irrational
negative_passages.docid: 101835
negative_passages.text: Which rationals can be written as the sum of two rational squares?
negative_passages.docid: 143733
negative_passages.text: Is this proof that $\sqrt 2$ is irrational correct?
negative_passages.docid: 84017
negative_passages.text: Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
negative_passages.docid: 92226
negative_passages.text: Prove $\sqrt6$ is irrational
negative_passages.docid: 7966
negative_passages.text: How prove $ \sqrt{2}+\sqrt{3}>\pi$?
negative_passages.docid: 32
negative_passages.text: Is $n^{th}$ root of $2$ an irrational number?