List questions from irrational-numbers

Published on 08 Feb 2016 - 0:53

111

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For what numbers $n$ is $\sqrt{n}$ irrational?

Published on 01 Apr 2026 - 17:11

552

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Square root of the product of consecutive natural numbers is irrational

Published on 08 Feb 2016 - 19:49

563

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Is $\arctan2$ irrational?

Published on 09 Feb 2016 - 11:30

1.2k

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Additivity Implies Homogeneity of Rational Scalars

Published on 10 Feb 2016 - 2:13

132

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Why are positive rational numbers countable but real numbers are not?

Published on 10 Feb 2016 - 22:23

4.1k

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Convergent sequence of irrational numbers that has a rational limit.

Published on 12 Feb 2016 - 18:13

45

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Shift of finitely many reals into irrationals

Published on 14 Feb 2016 - 4:41

394

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Swapping the digits of an algebraic number (e.g. $\sqrt 2$)

Published on 28 Mar 2026 - 2:22

703

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Elementary proof that $\pi$ is irrational

Published on 30 Mar 2026 - 10:35

239

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How to prove $a_{1}\sqrt[b_{1}]{c_{1}}+a_{2}\sqrt[b_{2}]{c_{2}}+.....+a_{n}\sqrt[b_{n}]{c_{n}}$ is irrational?

Published on 15 Feb 2016 - 22:13

1.3k

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Geometric proof for irrationality of $\pi$

Published on 16 Feb 2016 - 12:22

1.1k

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Given a rational number and an irrational number, both greater than 0, prove that the product between them is irrational.

Published on 17 Feb 2016 - 17:15

326

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The irrationality of $\sqrt[n]{2}$ from the FLT.

Published on 18 Feb 2016 - 3:35

188

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Arithmetic geometric mean - irrational, algebraic, trancendental?

Published on 30 Mar 2026 - 16:30

List Question

Is it true that $\mathbb{Q}(\sqrt{2}) \cap \mathbb{Q}(i) = \mathbb{Q}$?

For what numbers $n$ is $\sqrt{n}$ irrational?

Square root of the product of consecutive natural numbers is irrational

Is $\arctan2$ irrational?

Additivity Implies Homogeneity of Rational Scalars

Why are positive rational numbers countable but real numbers are not?

Convergent sequence of irrational numbers that has a rational limit.

Shift of finitely many reals into irrationals

Swapping the digits of an algebraic number (e.g. $\sqrt 2$)

Elementary proof that $\pi$ is irrational

How to prove $a_{1}\sqrt[b_{1}]{c_{1}}+a_{2}\sqrt[b_{2}]{c_{2}}+.....+a_{n}\sqrt[b_{n}]{c_{n}}$ is irrational?

Geometric proof for irrationality of $\pi$

Given a rational number and an irrational number, both greater than 0, prove that the product between them is irrational.

The irrationality of $\sqrt[n]{2}$ from the FLT.

Arithmetic geometric mean - irrational, algebraic, trancendental?

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