query: $n^x$, $x$ is irrational number what is the result?
positive_passages.docid: 7801
positive_passages.text: Can you raise a number to an irrational exponent?
negative_passages.docid: 91101
negative_passages.text: Proving $\sqrt2$ is irrational
negative_passages.docid: 124641
negative_passages.text: Prove that $5^{1/3}+7^{1/2}$ is irrational
negative_passages.docid: 69264
negative_passages.text: Is there an irrational number $a$ such that $a^a$ is rational?
negative_passages.docid: 118374
negative_passages.text: Is there a proof that $\pi$ is an irrational number?
negative_passages.docid: 89716
negative_passages.text: Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
negative_passages.docid: 20315
negative_passages.text: $\sqrt[31]{12} +\sqrt[12]{31}$ is irrational
negative_passages.docid: 26109
negative_passages.text: Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
negative_passages.docid: 15110
negative_passages.text: About irrational logarithms
negative_passages.docid: 132115
negative_passages.text: Verify my proof of the irrationality of $\sqrt{6}$.
negative_passages.docid: 158066
negative_passages.text: Prove $2^{1/3}$ is irrational.
negative_passages.docid: 143733
negative_passages.text: Is this proof that $\sqrt 2$ is irrational correct?
negative_passages.docid: 22762
negative_passages.text: How can adding an infinite number of rationals yield an irrational number?
negative_passages.docid: 37189
negative_passages.text: Exponent of a number is a square root?
negative_passages.docid: 58284
negative_passages.text: How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
negative_passages.docid: 39021
negative_passages.text: Proving that $\sqrt{2}+\sqrt{3}$ is irrational
negative_passages.docid: 150088
negative_passages.text: Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$