Question

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

score 215 · Answer 1 · 2026-04-15 03:25:06

215

Views

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

Published on 15 Apr 2026 - 3:25

score 592 · Answer 2 · 2026-04-16 09:36:31

592

Views

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

Published on 16 Apr 2026 - 9:36

score 494 · Answer 3 · 2026-04-14 09:13:15

494

Views

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

Published on 14 Apr 2026 - 9:13

score 262 · Answer 4 · 2026-04-15 20:02:57

262

Views

Irrationality of the concatenation of decimal expansions of primes

Published on 15 Apr 2026 - 20:02

score 124 · Answer 5 · 2026-04-15 07:40:51

124

Views

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

Published on 15 Apr 2026 - 7:40

score 132 · Answer 6 · 2026-04-16 09:11:53

132

Views

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

Published on 16 Apr 2026 - 9:11

score 60 · Answer 7 · 2026-04-16 20:52:08

60

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 16 Apr 2026 - 20:52

score 242 · Answer 8 · 2026-04-18 16:18:44

242

Views

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

Published on 18 Apr 2026 - 16:18

score 149 · Answer 9 · 2026-04-15 17:31:07

149

Views

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

Published on 15 Apr 2026 - 17:31

score 686 · Answer 10 · 2026-04-13 06:30:54

686

Views

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

Published on 13 Apr 2026 - 6:30

score 357 · Answer 11 · 2026-04-17 01:47:10

357

Views

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

Published on 17 Apr 2026 - 1:47

score 9.8k · Answer 12 · 2026-04-11 03:30:33

9.8k

Views

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

Published on 11 Apr 2026 - 3:30

score 1k · Answer 13 · 2026-05-10 16:12:49

1k

Views

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

Published on 10 May 2026 - 16:12

score 4.8k · Answer 14 · 2026-04-11 19:09:51

4.8k

Views

Proof that $\sin10^\circ$ is irrational

Published on 11 Apr 2026 - 19:09

score 74 · Answer 15 · 2026-04-14 22:38:39

74

Views

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

Published on 14 Apr 2026 - 22:38

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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