Question

When is $\sqrt[3]{a+\sqrt b}+\sqrt[3]{a-\sqrt b}$ an integer?

score 267 · Answer 1 · 2017-08-24 01:56:10

267

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When is $\sqrt[3]{a+\sqrt b}+\sqrt[3]{a-\sqrt b}$ an integer?

Published on 24 Aug 2017 - 1:56

score 288 · Answer 2 · 2026-03-31 01:04:05

288

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Is this true $n!\leq(\frac{5n+7}{12})^n,n∈N$?

Published on 31 Mar 2026 - 1:04

score 3k · Answer 3 · 2017-08-25 01:46:23

3k

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Find the value of $\frac{9}{5}(a+b)$ given that $a\sqrt{a}+b\sqrt{b}=183$ and $a\sqrt{b}+b\sqrt{a}=182$

Published on 25 Aug 2017 - 1:46

score 305 · Answer 4 · 2026-03-25 17:37:04

305

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Proof: $\cot(7.5^\circ) = \sqrt2 +\sqrt3 + \sqrt 4 + \sqrt6$

Published on 25 Mar 2026 - 17:37

score 86 · Answer 5 · 2026-04-12 12:28:57

86

Views

A simple question about an expression with square roots

Published on 12 Apr 2026 - 12:28

score 201 · Answer 6 · 2026-03-30 11:57:18

201

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Proving $\sqrt{3+\sqrt{13+4\sqrt{3}}} = 1+\sqrt{3}$.

Published on 30 Mar 2026 - 11:57

score 82 · Answer 7 · 2017-08-26 18:09:42

82

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inequality $\sqrt{\ln(3+x+y)} \le 2 \sqrt{\ln(3+x)} \sqrt{\ln(3+y)} \quad (x,y>0)$

Published on 26 Aug 2017 - 18:09

score 182 · Answer 8 · 2017-08-27 05:03:35

182

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Multiplying radicals by variables

Published on 27 Aug 2017 - 5:03

score 1.1k · Answer 9 · 2026-04-04 23:06:33

1.1k

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Need help with epsilon delta proof that $\lim_{x\to 2}\sqrt{4x-x^2}=2$

Published on 04 Apr 2026 - 23:06

score 302 · Answer 10 · 2026-04-06 11:37:28

302

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Simplify $\frac1{\sqrt{x^2+1}}-\frac{x^2}{(x^2+1)^{3/2}}$

Published on 06 Apr 2026 - 11:37

score 3.9k · Answer 11 · 2017-08-27 14:38:10

3.9k

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$x^2 + 3x + \frac{3}x + \frac{1}{x^2} = 26$ and $x$ can be written as $a + \sqrt{b}$ where $a$ and $b$ are positive integers, then find $a + b$.

Published on 27 Aug 2017 - 14:38

score 85 · Answer 12 · 2017-08-27 18:46:16

85

Views

Is it necessarily true that $x$ is forced to be nonnegative in the case of $\sqrt{x^3}$?

Published on 27 Aug 2017 - 18:46

score 2k · Answer 13 · 2026-04-10 07:16:13

2k

Views

Finding the largest square factor of an integer without complete factorization

Published on 10 Apr 2026 - 7:16

score 227 · Answer 14 · 2017-08-29 16:36:10

227

Views

Simplify $\sqrt{x^2-6x+9}-\sqrt{x^2+6x+9}$, if $x<0.$

Published on 29 Aug 2017 - 16:36

score 936 · Answer 15 · 2026-04-06 09:47:47

936

Views

Why does $\mathrm{abs}(i)=1$

Published on 06 Apr 2026 - 9:47

List Question

When is $\sqrt[3]{a+\sqrt b}+\sqrt[3]{a-\sqrt b}$ an integer?

Is this true $n!\leq(\frac{5n+7}{12})^n,n∈N$?

Find the value of $\frac{9}{5}(a+b)$ given that $a\sqrt{a}+b\sqrt{b}=183$ and $a\sqrt{b}+b\sqrt{a}=182$

Proof: $\cot(7.5^\circ) = \sqrt2 +\sqrt3 + \sqrt 4 + \sqrt6$

A simple question about an expression with square roots

Proving $\sqrt{3+\sqrt{13+4\sqrt{3}}} = 1+\sqrt{3}$.

inequality $\sqrt{\ln(3+x+y)} \le 2 \sqrt{\ln(3+x)} \sqrt{\ln(3+y)} \quad (x,y>0)$

Multiplying radicals by variables

Need help with epsilon delta proof that $\lim_{x\to 2}\sqrt{4x-x^2}=2$

Simplify $\frac1{\sqrt{x^2+1}}-\frac{x^2}{(x^2+1)^{3/2}}$

$x^2 + 3x + \frac{3}x + \frac{1}{x^2} = 26$ and $x$ can be written as $a + \sqrt{b}$ where $a$ and $b$ are positive integers, then find $a + b$.

Is it necessarily true that $x$ is forced to be nonnegative in the case of $\sqrt{x^3}$?

Finding the largest square factor of an integer without complete factorization

Simplify $\sqrt{x^2-6x+9}-\sqrt{x^2+6x+9}$, if $x<0.$

Why does $\mathrm{abs}(i)=1$

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