Question

Prove that $(\sqrt3+2)^m$ is not a natural number for all natural numbers $m≥1$

score 212 · Answer 1 · 2014-10-25 17:11:34

212

Views

Prove that $(\sqrt3+2)^m$ is not a natural number for all natural numbers $m≥1$

Published on 25 Oct 2014 - 17:11

score 589 · Answer 2 · 2014-10-27 22:32:29

589

Views

Show that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational

Published on 27 Oct 2014 - 22:32

score 491 · Answer 3 · 2014-10-28 18:12:27

491

Views

A necessary condition for a series of rational numbers to be irrational?

Published on 28 Oct 2014 - 18:12

score 259 · Answer 4 · 2014-10-29 14:06:03

259

Views

Irrationality of the concatenation of decimal expansions of primes

Published on 29 Oct 2014 - 14:06

score 121 · Answer 5 · 2014-10-30 15:15:32

121

Views

Find the values of $k$ for which $\sqrt{1+\frac{k}{n}}$ is irrational for all $n\in\mathbb N$

Published on 30 Oct 2014 - 15:15

score 128 · Answer 6 · 2014-11-01 09:22:46

128

Views

Is $\sqrt{m}$ irrational iff at least one prime occurs with an odd exponent in the factorisation of $m$?

Published on 01 Nov 2014 - 9:22

score 57 · Answer 7 · 2014-11-04 02:41:01

57

Views

Prove that $\sqrt m$ is irrational by showing that the set $\{n\in\mathbb N: n\sqrt m\in\mathbb N\}$ is empty

Published on 04 Nov 2014 - 2:41

score 238 · Answer 8 · 2014-11-05 16:43:49

238

Views

If $a$ and $b$ are distinct positive integers, is $\sqrt[a+b]{\dfrac ab}$ irrational?

Published on 05 Nov 2014 - 16:43

score 146 · Answer 9 · 2014-11-08 19:21:34

146

Views

Decide whether the $\sqrt{\sqrt{5}+3}+\sqrt{\sqrt{5}-2}$ is rational

Published on 08 Nov 2014 - 19:21

score 683 · Answer 10 · 2014-11-08 19:22:43

683

Views

Can any root, such as a square root or a cube root, be rational?

Published on 08 Nov 2014 - 19:22

score 353 · Answer 11 · 2014-11-12 04:39:52

353

Views

What is the name of this proof of, "$\sqrt{2}$ is irrational"?

Published on 12 Nov 2014 - 4:39

score 9.8k · Answer 12 · 2014-11-13 16:39:51

9.8k

Views

Understanding the proof of "$\sqrt{2}$ is irrational" by contradiction.

Published on 13 Nov 2014 - 16:39

score 1k · Answer 13 · 2026-03-25 06:11:58

1k

Views

Why is this proof that $\sqrt{2}$ is irrational titled as "Proof by infinite descent"?

Published on 25 Mar 2026 - 6:11

score 4.8k · Answer 14 · 2014-11-25 01:10:15

4.8k

Views

Proof that $\sin10^\circ$ is irrational

Published on 25 Nov 2014 - 1:10

score 71 · Answer 15 · 2014-11-30 23:58:33

71

Views

Can $x^{2q}$ be irrational for rational $x$ and $q$?

Published on 30 Nov 2014 - 23:58

List Question

Prove that $(\sqrt3+2)^m$ is not a natural number for all natural numbers $m≥1$

Show that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational

A necessary condition for a series of rational numbers to be irrational?

Irrationality of the concatenation of decimal expansions of primes

Find the values of $k$ for which $\sqrt{1+\frac{k}{n}}$ is irrational for all $n\in\mathbb N$

Is $\sqrt{m}$ irrational iff at least one prime occurs with an odd exponent in the factorisation of $m$?

Prove that $\sqrt m$ is irrational by showing that the set $\{n\in\mathbb N: n\sqrt m\in\mathbb N\}$ is empty

If $a$ and $b$ are distinct positive integers, is $\sqrt[a+b]{\dfrac ab}$ irrational?

Decide whether the $\sqrt{\sqrt{5}+3}+\sqrt{\sqrt{5}-2}$ is rational

Can any root, such as a square root or a cube root, be rational?

What is the name of this proof of, "$\sqrt{2}$ is irrational"?

Understanding the proof of "$\sqrt{2}$ is irrational" by contradiction.

Why is this proof that $\sqrt{2}$ is irrational titled as "Proof by infinite descent"?

Proof that $\sin10^\circ$ is irrational

Can $x^{2q}$ be irrational for rational $x$ and $q$?

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