Question

Prove $\sqrt[n]{x^n} =x$ when $n$ is odd and $\sqrt[n]{x^n}=|x|$ when $n$ is even.

score 105 · Answer 1 · 2026-04-17 05:24:05

105

Views

Prove $\sqrt[n]{x^n} =x$ when $n$ is odd and $\sqrt[n]{x^n}=|x|$ when $n$ is even.

Published on 17 Apr 2026 - 5:24

score 68 · Answer 2 · 2026-04-11 09:53:05

68

Views

$n$-th roots in a group

Published on 11 Apr 2026 - 9:53

score 70 · Answer 3 · 2026-04-15 20:37:38

70

Views

When is $\sqrt{n-\sqrt{m}}=\sqrt{a}-\sqrt{b}$ where $m,n\in\Bbb{Z}^+$ and $a,b\in\Bbb{Q}$?

Published on 15 Apr 2026 - 20:37

score 47 · Answer 4 · 2026-03-25 07:42:43

47

Views

Is there a general theorem relating the Dedekind eta function to polynomial roots?

Published on 25 Mar 2026 - 7:42

score 213 · Answer 5 · 2026-04-17 12:09:36

213

Views

On generalizing $\frac{17-\sqrt{17}}8 =\sin^2(t)+\sin^2(2t)+\sin^2(4t)+\sin^2(8t)$?

Published on 17 Apr 2026 - 12:09

score 112 · Answer 6 · 2026-04-17 09:40:57

112

Views

On fundamental units and generalizing $\left(\frac{3+\sqrt{13}}2\right)^{3/2} =\frac{\tan(t)\tan(3t)\tan(4t)}{\sqrt[4]{13}}$

Published on 17 Apr 2026 - 9:40

score 58 · Answer 7 · 2026-04-17 00:31:43

58

Views

Equality of functions $f(x)=x^\frac{m}{n}$ and $g(x)= \sqrt[n]{x^m}$

Published on 17 Apr 2026 - 0:31

score 97 · Answer 8 · 2026-04-13 04:26:07

97

Views

$[L:K]=2$ and $char(K)\neq 2$ $\Rightarrow$ $L=K(\sqrt{a})$ for an $a \in K$.

Published on 13 Apr 2026 - 4:26

score 69 · Answer 9 · 2026-04-10 12:48:47

69

Views

Problems finding the n-th root of a negative number

Published on 10 Apr 2026 - 12:48

score 98 · Answer 10 · 2026-04-13 21:32:12

98

Views

Find the greatest integer in the expression below as a function of the given conditions

Published on 13 Apr 2026 - 21:32

score 264 · Answer 11 · 2026-04-15 13:09:26

264

Views

Efficently calculating the "integer hypotenuse"

Published on 15 Apr 2026 - 13:09

score 122 · Answer 12 · 2026-04-14 08:38:53

122

Views

Does $\sqrt {-9} = -(9^{1/2})\;?$

Published on 14 Apr 2026 - 8:38

score 42 · Answer 13 · 2026-04-15 21:15:21

42

Views

prove the following statement $|a-b| \le 2\sqrt{a}c + d$ implies $a \le \varepsilon a/(1+\varepsilon) + (1+\varepsilon)c^2/\varepsilon + (b + d)$

Published on 15 Apr 2026 - 21:15

score 206 · Answer 14 · 2026-04-11 01:06:23

206

Views

Where is error in this solution to $ \sqrt{x} + \sqrt{-x} = 2 $?

Published on 11 Apr 2026 - 1:06

score 182 · Answer 15 · 2026-04-15 11:42:18

182

Views

Galois group of the quintic $x^5 -11x + 1$.

Published on 15 Apr 2026 - 11:42

List Question

Prove $\sqrt[n]{x^n} =x$ when $n$ is odd and $\sqrt[n]{x^n}=|x|$ when $n$ is even.

$n$-th roots in a group

When is $\sqrt{n-\sqrt{m}}=\sqrt{a}-\sqrt{b}$ where $m,n\in\Bbb{Z}^+$ and $a,b\in\Bbb{Q}$?

Is there a general theorem relating the Dedekind eta function to polynomial roots?

On generalizing $\frac{17-\sqrt{17}}8 =\sin^2(t)+\sin^2(2t)+\sin^2(4t)+\sin^2(8t)$?

On fundamental units and generalizing $\left(\frac{3+\sqrt{13}}2\right)^{3/2} =\frac{\tan(t)\tan(3t)\tan(4t)}{\sqrt[4]{13}}$

Equality of functions $f(x)=x^\frac{m}{n}$ and $g(x)= \sqrt[n]{x^m}$

$[L:K]=2$ and $char(K)\neq 2$ $\Rightarrow$ $L=K(\sqrt{a})$ for an $a \in K$.

Problems finding the n-th root of a negative number

Find the greatest integer in the expression below as a function of the given conditions

Efficently calculating the "integer hypotenuse"

Does $\sqrt {-9} = -(9^{1/2})\;?$

prove the following statement $|a-b| \le 2\sqrt{a}c + d$ implies $a \le \varepsilon a/(1+\varepsilon) + (1+\varepsilon)c^2/\varepsilon + (b + d)$

Where is error in this solution to $ \sqrt{x} + \sqrt{-x} = 2 $?

Galois group of the quintic $x^5 -11x + 1$.

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