List questions from rationality-testing

Published on 03 Oct 2014 - 3:51

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Decide if radical expression equals a given rational number

Published on 06 Oct 2014 - 10:46

447

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Show that $(\sqrt{2}-1)^n$ is irrational

Published on 09 Oct 2014 - 15:20

144

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Proof of $\sqrt{n^2-4}, n\ge 3$ being irrational

Published on 09 Oct 2014 - 16:27

131

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Quotient of two rational sequences and the nature of its limit

Published on 24 Mar 2026 - 8:48

3.1k

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Is $x^y$ always irrational if $x$ is rational and $y$ is irrational?

Published on 16 Oct 2014 - 23:48

434

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If $x$ is a positive rational but not an integer, is $x^x$ irrational?

Published on 17 Oct 2014 - 12:52

2.5k

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Proving the irrationality of $\sqrt{5}$: if $5$ divides $x^2$, then $5$ divides $x$

Published on 17 Oct 2014 - 18:32

36k

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The square root of a prime number is irrational

Published on 18 Oct 2014 - 8:44

86

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If $x^3 =7$, then $x$ is irrational

Published on 19 Oct 2014 - 19:46

777

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Irrationality of sum of two logarithms: $\log_2 5 +\log_3 5$

Published on 22 Oct 2014 - 18:00

5.9k

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If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?

Published on 23 Oct 2014 - 15:38

23.6k

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How to show that the product of two irrational numbers may be irrational?

Published on 24 Oct 2014 - 2:19

1.6k

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For which $x$ is $e^x$ rational? Transcendental?

Published on 23 Mar 2026 - 18:03

293

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Is this sum of 2 different irrational logarithms irrational: $\log_2(3)+\log_3(2)$?

Published on 24 Oct 2014 - 20:17

List Question

Is $x^{1-\frac{1}{n}}+ (1-x)^{1-\frac{1}{n}}$ always irrational if $x$ is rational?

Decide if radical expression equals a given rational number

Show that $(\sqrt{2}-1)^n$ is irrational

Proof of $\sqrt{n^2-4}, n\ge 3$ being irrational

Quotient of two rational sequences and the nature of its limit

Is $x^y$ always irrational if $x$ is rational and $y$ is irrational?

If $x$ is a positive rational but not an integer, is $x^x$ irrational?

Proving the irrationality of $\sqrt{5}$: if $5$ divides $x^2$, then $5$ divides $x$

The square root of a prime number is irrational

If $x^3 =7$, then $x$ is irrational

Irrationality of sum of two logarithms: $\log_2 5 +\log_3 5$

If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?

How to show that the product of two irrational numbers may be irrational?

For which $x$ is $e^x$ rational? Transcendental?

Is this sum of 2 different irrational logarithms irrational: $\log_2(3)+\log_3(2)$?

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