Question

Show that $\{1, \sqrt{2}, \sqrt{3}\}$ is linearly independent over $\mathbb{Q}$.

score 4.9k · Answer 1 · 2013-11-09 13:47:40

4.9k

Views

Show that $\{1, \sqrt{2}, \sqrt{3}\}$ is linearly independent over $\mathbb{Q}$.

Published on 09 Nov 2013 - 13:47

score 134 · Answer 2 · 2013-11-11 00:42:40

134

Views

Can the exponentiation of an integer by a rational be a non-integer rational?

Published on 11 Nov 2013 - 0:42

score 321 · Answer 3 · 2026-04-04 12:10:59

321

Views

Is the fraction of the irrational exponentiations of two coprime integers by a rational an irrational?

Published on 04 Apr 2026 - 12:10

score 457 · Answer 4 · 2013-11-11 15:21:14

457

Views

Can you get any irrational number using square roots?

Published on 11 Nov 2013 - 15:21

score 352 · Answer 5 · 2013-11-12 19:01:01

352

Views

The shape of a graph of a function with $n$th-roots?

Published on 12 Nov 2013 - 19:01

score 153 · Answer 6 · 2013-11-17 17:22:53

153

Views

Does $\pi \ | \ 2 \pi$

Published on 17 Nov 2013 - 17:22

score 86 · Answer 7 · 2013-11-19 04:09:33

86

Views

Existence of five real numbers satisfying a given condition.

Published on 19 Nov 2013 - 4:09

score 1.3k · Answer 8 · 2026-03-31 23:55:51

1.3k

Views

$\arctan$ of a square root as a rational multiple of $\pi$

Published on 31 Mar 2026 - 23:55

score 382 · Answer 9 · 2013-11-25 17:08:55

382

Views

Determine if the number $ \sqrt{8+2\sqrt{10+2\sqrt{5}}} - \sqrt{8-2\sqrt{10+2\sqrt{5}}} $ is rational

Published on 25 Nov 2013 - 17:08

score 75 · Answer 10 · 2013-11-26 10:52:52

75

Views

recipe for infinitely many irrational numbers - or is it?

Published on 26 Nov 2013 - 10:52

score 83 · Answer 11 · 2013-11-26 15:38:14

83

Views

probability that a number defined by a random process is irrational

Published on 26 Nov 2013 - 15:38

score 632 · Answer 12 · 2013-11-29 10:26:27

632

Views

If $\beta=0.{a_1}^{k}{a_2}^{k}{a_3}^{k}\cdots\in\mathbb Q$, then $\alpha=0.a_1a_2a_3\cdots\in\mathbb Q$?

Published on 29 Nov 2013 - 10:26

score 102 · Answer 13 · 2013-12-01 22:59:15

102

Views

Does $E^2 \; ( E \approx 1.2640847\ldots)$ equal $D \approx 1.5979102\ldots$?

Published on 01 Dec 2013 - 22:59

score 4.4k · Answer 14 · 2013-12-02 06:11:32

4.4k

Views

Sum of all real number for any interval.

Published on 02 Dec 2013 - 6:11

score 4.7k · Answer 15 · 2013-12-06 01:14:34

4.7k

Views

How to represent the square root of 90 as a fraction?

Published on 06 Dec 2013 - 1:14

List Question

Show that $\{1, \sqrt{2}, \sqrt{3}\}$ is linearly independent over $\mathbb{Q}$.

Can the exponentiation of an integer by a rational be a non-integer rational?

Is the fraction of the irrational exponentiations of two coprime integers by a rational an irrational?

Can you get any irrational number using square roots?

The shape of a graph of a function with $n$th-roots?

Does $\pi \ | \ 2 \pi$

Existence of five real numbers satisfying a given condition.

$\arctan$ of a square root as a rational multiple of $\pi$

Determine if the number $ \sqrt{8+2\sqrt{10+2\sqrt{5}}} - \sqrt{8-2\sqrt{10+2\sqrt{5}}} $ is rational

recipe for infinitely many irrational numbers - or is it?

probability that a number defined by a random process is irrational

If $\beta=0.{a_1}^{k}{a_2}^{k}{a_3}^{k}\cdots\in\mathbb Q$, then $\alpha=0.a_1a_2a_3\cdots\in\mathbb Q$?

Does $E^2 \; ( E \approx 1.2640847\ldots)$ equal $D \approx 1.5979102\ldots$?

Sum of all real number for any interval.

How to represent the square root of 90 as a fraction?

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