Question

How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?

score 45.8k · Answer 1 · 2026-04-15 12:55:10

45.8k

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How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?

Published on 15 Apr 2026 - 12:55

score 14.1k · Answer 2 · 2026-04-14 06:31:47

14.1k

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Integral of $\sqrt{1 + \sqrt{x}}$

Published on 14 Apr 2026 - 6:31

score 560 · Answer 3 · 2026-03-26 11:47:53

560

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Rationalising the denominator: $\frac{11}{3\sqrt{3}+7}$

Published on 26 Mar 2026 - 11:47

score 697 · Answer 4 · 2026-04-17 07:14:37

697

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How to prove $\left(\frac{4}{3-\sqrt{5}}\right)^2 - \left(\frac{6 - 5 \sqrt{6}}{5 - \sqrt{6}}\right)^2 = 2\sqrt{61+24\sqrt{5}}$?

Published on 17 Apr 2026 - 7:14

score 3.8k · Answer 5 · 2026-04-17 10:34:53

3.8k

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For $n \in \mathbb{N}$ $\lfloor{\sqrt{n} + \sqrt{n+1}\rfloor} = \lfloor{\sqrt{4n+2}\rfloor}$

Published on 17 Apr 2026 - 10:34

score 258 · Answer 6 · 2026-04-15 19:04:43

258

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Finding all real solutions to $ \sqrt{x^2-p}+2\sqrt{x^2-1}=x $

Published on 15 Apr 2026 - 19:04

score 3.2k · Answer 7 · 2026-04-11 22:43:43

3.2k

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Floor of Square Root Summation problem

Published on 11 Apr 2026 - 22:43

score 17.8k · Answer 8 · 2026-04-14 07:31:29

17.8k

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How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$

Published on 14 Apr 2026 - 7:31

score 9k · Answer 9 · 2026-04-12 21:26:43

9k

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Is $n^{th}$ root of $2$ an irrational number?

Published on 12 Apr 2026 - 21:26

score 732 · Answer 10 · 2026-04-15 19:22:08

732

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Series $\sum_{n=1}^{\infty} (\sqrt[3]{n+1} - \sqrt[3]{n-1})^{\alpha}$ converge or diverge?

Published on 15 Apr 2026 - 19:22

score 5.6k · Answer 11 · 2026-04-16 15:42:19

5.6k

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Significance of $\sqrt[n]{a^n} $?!

Published on 16 Apr 2026 - 15:42

score 10.9k · Answer 12 · 2026-04-09 23:01:14

10.9k

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Square roots -- positive and negative

Published on 09 Apr 2026 - 23:01

score 21.3k · Answer 13 · 2026-04-14 13:03:25

21.3k

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Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$

Published on 14 Apr 2026 - 13:03

score 14.4k · Answer 14 · 2026-04-14 02:36:22

14.4k

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Finding the limit of $\frac {n}{\sqrt[n]{n!}}$

Published on 14 Apr 2026 - 2:36

score 5.8k · Answer 15 · 2026-04-16 11:25:19

5.8k

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Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$

Published on 16 Apr 2026 - 11:25

List Question

How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?

Integral of $\sqrt{1 + \sqrt{x}}$

Rationalising the denominator: $\frac{11}{3\sqrt{3}+7}$

How to prove $\left(\frac{4}{3-\sqrt{5}}\right)^2 - \left(\frac{6 - 5 \sqrt{6}}{5 - \sqrt{6}}\right)^2 = 2\sqrt{61+24\sqrt{5}}$?

For $n \in \mathbb{N}$ $\lfloor{\sqrt{n} + \sqrt{n+1}\rfloor} = \lfloor{\sqrt{4n+2}\rfloor}$

Finding all real solutions to $ \sqrt{x^2-p}+2\sqrt{x^2-1}=x $

Floor of Square Root Summation problem

How to prove that: $\tan(3\pi/11) + 4\sin(2\pi/11) = \sqrt{11}$

Is $n^{th}$ root of $2$ an irrational number?

Series $\sum_{n=1}^{\infty} (\sqrt[3]{n+1} - \sqrt[3]{n-1})^{\alpha}$ converge or diverge?

Significance of $\sqrt[n]{a^n} $?!

Square roots -- positive and negative

Proof of $\lim_{n\to \infty} \sqrt[n]{n}=1$

Finding the limit of $\frac {n}{\sqrt[n]{n!}}$

Limits: How to evaluate $\lim\limits_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$

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