List questions from rationality-testing

Published on 16 Apr 2026 - 12:24

84

Views

Decide if radical expression equals a given rational number

Published on 15 Apr 2026 - 10:25

449

Views

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

Published on 14 Apr 2026 - 18:46

147

Views

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

Published on 16 Apr 2026 - 5:26

133

Views

Quotient of two rational sequences and the nature of its limit

Published on 25 Mar 2026 - 13:52

3.1k

Views

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

Published on 15 Apr 2026 - 2:45

437

Views

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

Published on 14 Apr 2026 - 3:43

2.5k

Views

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

Published on 17 Apr 2026 - 1:26

36k

Views

The square root of a prime number is irrational

Published on 17 Apr 2026 - 11:18

89

Views

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

Published on 16 Apr 2026 - 2:35

779

Views

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

Published on 10 May 2026 - 17:15

5.9k

Views

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

Published on 16 Apr 2026 - 13:04

23.6k

Views

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

Published on 09 Apr 2026 - 17:49

1.6k

Views

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

Published on 25 Mar 2026 - 13:16

296

Views

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

Published on 16 Apr 2026 - 3:50

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: $\log_2(3)+\log_3(2)$?

Trending Questions

Popular # Hahtags

Popular Questions