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All Solutions for $(-256)^{\frac{1}{4}}$ and $1^{\frac{1}{5}}$ Imaginary Roots?

score 5.4k · Answer 1 · 2026-03-29 14:32:27

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All Solutions for $(-256)^{\frac{1}{4}}$ and $1^{\frac{1}{5}}$ Imaginary Roots?

Published on 29 Mar 2026 - 14:32

score 266 · Answer 2 · 2015-12-31 12:39:52

266

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How to solve the integral $\int\frac{x-1}{\sqrt{ x^2-2x}}dx $

Published on 31 Dec 2015 - 12:39

score 4k · Answer 3 · 2016-01-01 08:53:42

4k

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Prove that $a\sqrt{a^2+bc}+b\sqrt{b^2+ac}+c\sqrt{c^2+ab}\geq\sqrt{2(a^2+b^2+c^2)(ab+ac+bc)}$

Published on 01 Jan 2016 - 8:53

score 349 · Answer 4 · 2026-04-04 08:46:25

349

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I need help to advance in the resolution of that limit: $ \lim_{n \to \infty}{\sqrt[n]{\frac{n!}{n^n}}} $

Published on 04 Apr 2026 - 8:46

score 288 · Answer 5 · 2026-04-06 01:24:18

288

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Integrate the square root of the ratio of two quadratic polynomials

Published on 06 Apr 2026 - 1:24

score 949 · Answer 6 · 2026-04-04 08:41:22

949

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Which is larger, $\sqrt[2015]{2015!}$ or $\sqrt[2016]{2016!}$?

Published on 04 Apr 2026 - 8:41

score 664 · Answer 7 · 2026-03-31 05:36:42

664

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solving $\int \frac{dx}{\sqrt{-x^2-12x+28}}$

Published on 31 Mar 2026 - 5:36

score 1.1k · Answer 8 · 2016-01-04 22:05:30

1.1k

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Prove that limit of the fractional part of $\sqrt{n^2+n}$ is $\frac{1}{2}$

Published on 04 Jan 2016 - 22:05

score 453 · Answer 9 · 2016-01-05 03:03:36

453

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Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$

Published on 05 Jan 2016 - 3:03

score 2.6k · Answer 10 · 2026-04-07 05:34:56

2.6k

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Prove that $a^2+b^2+c^2+3\sqrt[3]{a^2b^2c^2} \geq 2(ab+bc+ca).$

Published on 07 Apr 2026 - 5:34

score 1.9k · Answer 11 · 2026-04-03 01:56:54

1.9k

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Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$.

Published on 03 Apr 2026 - 1:56

score 229 · Answer 12 · 2016-01-06 13:57:31

229

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Finding a limit with negative infinity (Square root)

Published on 06 Jan 2016 - 13:57

score 320 · Answer 13 · 2026-03-26 23:13:29

320

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How to solve $x^4+8x-1=0 $

Published on 26 Mar 2026 - 23:13

score 4.3k · Answer 14 · 2026-03-29 14:30:59

4.3k

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Why do I get an imaginary result for the cube root of a negative number?

Published on 29 Mar 2026 - 14:30

score 79 · Answer 15 · 2016-01-07 00:22:33

79

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How to solve the following arithmetic radical problem?

Published on 07 Jan 2016 - 0:22

List Question

All Solutions for $(-256)^{\frac{1}{4}}$ and $1^{\frac{1}{5}}$ Imaginary Roots?

How to solve the integral $\int\frac{x-1}{\sqrt{ x^2-2x}}dx $

Prove that $a\sqrt{a^2+bc}+b\sqrt{b^2+ac}+c\sqrt{c^2+ab}\geq\sqrt{2(a^2+b^2+c^2)(ab+ac+bc)}$

I need help to advance in the resolution of that limit: $ \lim_{n \to \infty}{\sqrt[n]{\frac{n!}{n^n}}} $

Integrate the square root of the ratio of two quadratic polynomials

Which is larger, $\sqrt[2015]{2015!}$ or $\sqrt[2016]{2016!}$?

solving $\int \frac{dx}{\sqrt{-x^2-12x+28}}$

Prove that limit of the fractional part of $\sqrt{n^2+n}$ is $\frac{1}{2}$

Show that $\frac{a^2}{\sqrt{(1+a^3)(1+b^3)}}+\frac{b^2}{\sqrt{(1+b^3)(1+c^3)}}+\frac{c^2}{\sqrt{(1+c^3)(1+a^3)}} \geq \frac{4}{3}$

Prove that $a^2+b^2+c^2+3\sqrt[3]{a^2b^2c^2} \geq 2(ab+bc+ca).$

Use the Cauchy-Schwarz Inequality to prove that $a^2+b^2+c^2 \ge ab+ac+bc $ for all positive $a,b,c$.

Finding a limit with negative infinity (Square root)

How to solve $x^4+8x-1=0 $

Why do I get an imaginary result for the cube root of a negative number?

How to solve the following arithmetic radical problem?

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