List questions from rationality-testing

Published on 09 Dec 2014 - 7:05

631

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Prove that $\sqrt{n^2 + 2}$ is irrational

Published on 10 Dec 2014 - 6:14

2.6k

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Alternate proof for "$\log_{10}{2}$ is irrational"

Published on 14 Dec 2014 - 5:16

3.6k

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A real number $x$ such that $x^n$ and $(x+1)^n$ are rational is itself rational

Published on 15 Dec 2014 - 22:28

752

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Simple proof that $\pi$ is irrational - using prime factors of denominator

Published on 21 Dec 2014 - 20:25

133

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If $a$ is irrational, does there exist a natural number $n$ such that $na$ is rational?

Published on 29 Dec 2014 - 12:38

649

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Is the sum of all irrational numbers between two integers rational?

Published on 31 Dec 2014 - 5:43

302

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How to evaluate a sum which contains limit variables?

Published on 31 Dec 2014 - 20:35

68

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On $p^{\log_q n}$, where $p$ and $q$ are distinct primes

Published on 25 Mar 2026 - 14:27

819

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$\sqrt{6}-\sqrt{2}-\sqrt{3}$ is irrational

Published on 08 Oct 2019 - 11:00

26

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Can there exist two different prime numbers, such that their roots added together equal a rational number?

Published on 16 Nov 2019 - 17:49

57

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Formula for "cleanliness" or "roundness" of fraction

Published on 18 Nov 2019 - 15:26

638

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Show that there is no rational number whose square is $2$ or $8$

Published on 30 Nov 2019 - 7:19

189

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Prove that the ratio of acute angles in a $3:4:5$ triangle is irrational

Published on 01 Dec 2019 - 22:55

63

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Area inside $|x|^G+|y|^G=r^G$ is an integer multiple of $r^2$

Published on 10 Dec 2019 - 7:55

List Question

The cube of at least one irrational number is rational

Prove that $\sqrt{n^2 + 2}$ is irrational

Alternate proof for "$\log_{10}{2}$ is irrational"

A real number $x$ such that $x^n$ and $(x+1)^n$ are rational is itself rational

Simple proof that $\pi$ is irrational - using prime factors of denominator

If $a$ is irrational, does there exist a natural number $n$ such that $na$ is rational?

Is the sum of all irrational numbers between two integers rational?

How to evaluate a sum which contains limit variables?

On $p^{\log_q n}$, where $p$ and $q$ are distinct primes

$\sqrt{6}-\sqrt{2}-\sqrt{3}$ is irrational

Can there exist two different prime numbers, such that their roots added together equal a rational number?

Formula for "cleanliness" or "roundness" of fraction

Show that there is no rational number whose square is $2$ or $8$

Prove that the ratio of acute angles in a $3:4:5$ triangle is irrational

Area inside $|x|^G+|y|^G=r^G$ is an integer multiple of $r^2$

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