List questions from rationality-testing

Published on 08 Jan 2015 - 13:28

71

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Is there a systematic method of knowing if $n = \sqrt a $ is or is not a rational number?

Published on 12 Jan 2015 - 23:13

266

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Prove that $e^n$ is irrational for any natural number $n$

Published on 13 Jan 2015 - 7:50

248

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Proof of the rationality of $e + \pi$ via their series representation?

Published on 14 Jan 2015 - 3:56

387

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$\log_2 13$ is irrational

Published on 16 Jan 2015 - 14:21

1.1k

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Is this attempt of showing the square root of two is irrational valid?

Published on 26 Mar 2026 - 7:59

456

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Is $\sum_{n=1}^\infty \frac{1}{2^{n^2}}$ is rational number?

Published on 19 Jan 2015 - 16:36

4k

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Prove that the quotient of a nonzero rational number and an irrational number is irrational

Published on 26 Jan 2015 - 20:30

415

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For which $q\in\mathbb Q$ is $\sin(\frac\pi2q)$ rational?

Published on 27 Jan 2015 - 22:03

291

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Does there exist any positive integer $n$ such that $e^n$ is an integer (to show $\log 2$ is irrational)?

Published on 02 Feb 2015 - 14:39

2.5k

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Proof that the square root of $5$ is not a natural number

Published on 04 Feb 2015 - 0:28

148

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Is there a number $x\neq0$ whose products with $\pi$ and with $e$ are both rational?

Published on 12 Feb 2015 - 11:08

171

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Proving $ \sum_{k=1}^{\infty}\frac{9}{10^{\frac{k(k+1)}{2}}}=0.90900900090... $ is irrational

Published on 15 Feb 2015 - 7:04

451

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Is $\frac{\sqrt7}{\sqrt[3]{15}}$ rational or irrational?

Published on 27 Feb 2015 - 1:21

2.2k

Views

Is there a way, in general, to tell whether the nth root of a integer is rational?

Published on 04 Mar 2015 - 0:38

List Question

Can both $x$ and $\sin(x)$ be rational at the same time?

Is there a systematic method of knowing if $n = \sqrt a $ is or is not a rational number?

Prove that $e^n$ is irrational for any natural number $n$

Proof of the rationality of $e + \pi$ via their series representation?

$\log_2 13$ is irrational

Is this attempt of showing the square root of two is irrational valid?

Is $\sum_{n=1}^\infty \frac{1}{2^{n^2}}$ is rational number?

Prove that the quotient of a nonzero rational number and an irrational number is irrational

For which $q\in\mathbb Q$ is $\sin(\frac\pi2q)$ rational?

Does there exist any positive integer $n$ such that $e^n$ is an integer (to show $\log 2$ is irrational)?

Proof that the square root of $5$ is not a natural number

Is there a number $x\neq0$ whose products with $\pi$ and with $e$ are both rational?

Proving $ \sum_{k=1}^{\infty}\frac{9}{10^{\frac{k(k+1)}{2}}}=0.90900900090... $ is irrational

Is $\frac{\sqrt7}{\sqrt[3]{15}}$ rational or irrational?

Is there a way, in general, to tell whether the nth root of a integer is rational?

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