Question

How to prove this $\sum\limits_{cyc}a\sqrt{b^2+(n^2-1)c^2}\le (a+b+c)^2+(n-3)(ab+bc+ca)$

score 72 · Answer 1 · 2026-03-25 11:16:50

72

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How to prove this $\sum\limits_{cyc}a\sqrt{b^2+(n^2-1)c^2}\le (a+b+c)^2+(n-3)(ab+bc+ca)$

Published on 25 Mar 2026 - 11:16

score 275 · Answer 2 · 2016-10-21 12:41:03

275

Views

What are the $393$ trillion possible answers when computing $13^{th}$ root of a number?

Published on 21 Oct 2016 - 12:41

score 212 · Answer 3 · 2026-03-28 21:26:51

212

Views

Arithmetic Mean/Geometrix Mean Inequality of Degree 3

Published on 28 Mar 2026 - 21:26

score 82 · Answer 4 · 2026-03-28 23:55:50

82

Views

Solving radical questions

Published on 28 Mar 2026 - 23:55

score 52 · Answer 5 · 2016-10-22 14:32:37

52

Views

why does calculators consider the negative value of the square root as an imaginary part?

Published on 22 Oct 2016 - 14:32

score 8.8k · Answer 6 · 2026-03-27 05:04:06

8.8k

Views

$\sqrt{3}$ represented as continued fraction

Published on 27 Mar 2026 - 5:04

score 154 · Answer 7 · 2016-10-23 11:40:04

154

Views

Limit $\lim_{n\to\infty}\sqrt n(\sqrt[n]x-1)$

Published on 23 Oct 2016 - 11:40

score 299 · Answer 8 · 2026-03-25 14:25:24

299

Views

Combinatorial proof of a relation between the number of distinct prime divisors of a number and the Riemann zeta function.

Published on 25 Mar 2026 - 14:25

score 70 · Answer 9 · 2016-10-24 02:48:18

70

Views

Simplifying this radical

Published on 24 Oct 2016 - 2:48

score 273 · Answer 10 · 2026-03-28 09:57:14

273

Views

Let's prove this inequality, with/without induction $\sum\limits_{i=1}^n\frac1i \le \sqrt n$

Published on 28 Mar 2026 - 9:57

score 323 · Answer 11 · 2016-10-25 07:57:56

323

Views

Cube root of n is irrational or natural

Published on 25 Oct 2016 - 7:57

score 63 · Answer 12 · 2016-10-25 13:04:20

63

Views

Rationalising a denominator

Published on 25 Oct 2016 - 13:04

score 82 · Answer 13 · 2016-10-26 14:16:41

82

Views

If there's a specific algorithm to calculate roots (√) on calculators, why can't we just derive a formula from that algorithm?

Published on 26 Oct 2016 - 14:16

score 526 · Answer 14 · 2026-03-26 01:09:25

526

Views

Show that $\sqrt{q}$ is irrational

Published on 26 Mar 2026 - 1:09

score 70 · Answer 15 · 2026-03-31 05:32:44

70

Views

Find all such $b\in\mathbb{Z}_+$ that for all $n\in\mathbb{Z}_+$ there exists $y\in\mathbb{Z}_+$ such that $b^n+1=2y^3$

Published on 31 Mar 2026 - 5:32

List Question

How to prove this $\sum\limits_{cyc}a\sqrt{b^2+(n^2-1)c^2}\le (a+b+c)^2+(n-3)(ab+bc+ca)$

What are the $393$ trillion possible answers when computing $13^{th}$ root of a number?

Arithmetic Mean/Geometrix Mean Inequality of Degree 3

Solving radical questions

why does calculators consider the negative value of the square root as an imaginary part?

$\sqrt{3}$ represented as continued fraction

Limit $\lim_{n\to\infty}\sqrt n(\sqrt[n]x-1)$

Combinatorial proof of a relation between the number of distinct prime divisors of a number and the Riemann zeta function.

Simplifying this radical

Let's prove this inequality, with/without induction $\sum\limits_{i=1}^n\frac1i \le \sqrt n$

Cube root of n is irrational or natural

Rationalising a denominator

If there's a specific algorithm to calculate roots (√) on calculators, why can't we just derive a formula from that algorithm?

Show that $\sqrt{q}$ is irrational

Find all such $b\in\mathbb{Z}_+$ that for all $n\in\mathbb{Z}_+$ there exists $y\in\mathbb{Z}_+$ such that $b^n+1=2y^3$

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