Question

Combining a radical and simplifying?

score 59 · Answer 1 · 2026-04-09 17:48:35

59

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Combining a radical and simplifying?

Published on 09 Apr 2026 - 17:48

score 633 · Answer 2 · 2026-04-17 01:33:13

633

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Find the limit of: $\lim_{n\to\infty} \frac{1}{\sqrt[n+1]{(n+1)!} - \sqrt[n]{(n)!}}$

Published on 17 Apr 2026 - 1:33

score 189 · Answer 3 · 2026-04-17 05:53:16

189

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How can I calculate this limit: $\lim\limits_{x\rightarrow 2}\frac{2-\sqrt{2+x}}{2^{\frac{1}{3}}-(4-x)^\frac{1}{3}}$?

Published on 17 Apr 2026 - 5:53

score 8.3k · Answer 4 · 2026-04-15 19:21:00

8.3k

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Limit of a sequence involving root of a factorial: $\lim_{n \to \infty} \frac{n}{ \sqrt [n]{n!}}$

Published on 15 Apr 2026 - 19:21

score 1.9k · Answer 5 · 2026-03-26 11:47:53

1.9k

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Rationalize and simplify $\frac{x-1}{\sqrt{2\sqrt{x}} + 1 - \sqrt[4]{x}}$

Published on 26 Mar 2026 - 11:47

score 6.5k · Answer 6 · 2026-04-16 01:33:55

6.5k

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Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational

Published on 16 Apr 2026 - 1:33

score 434 · Answer 7 · 2026-04-16 11:48:08

434

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$\sqrt{x} +y = 4$, $x+ \sqrt{y}= 6$, find the solution $(x,y)$

Published on 16 Apr 2026 - 11:48

score 120 · Answer 8 · 2026-04-15 00:12:21

120

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Range of the solutions for $\sqrt{x} + \sqrt{x+16} = 3$

Published on 15 Apr 2026 - 0:12

score 1.1k · Answer 9 · 2026-04-15 03:31:44

1.1k

Views

Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$

Published on 15 Apr 2026 - 3:31

score 454 · Answer 10 · 2026-04-11 08:49:43

454

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Limit (without series expansion and l'Hôpital's rule)

Published on 11 Apr 2026 - 8:49

score 815 · Answer 11 · 2012-09-06 19:12:44

815

Views

Divergence of the harmonic series and the Cauchy criterion imply $\lim_{n\to\infty} \sqrt[n]n=1$

Published on 06 Sep 2012 - 19:12

score 3.6k · Answer 12 · 2026-04-15 11:22:02

3.6k

Views

Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.

Published on 15 Apr 2026 - 11:22

score 960 · Answer 13 · 2026-04-15 09:22:38

960

Views

Finding $\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$

Published on 15 Apr 2026 - 9:22

score 1.4k · Answer 14 · 2026-04-15 16:53:08

1.4k

Views

Limit of quotients with square roots: $\lim_{x\to2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}$

Published on 15 Apr 2026 - 16:53

score 21.8k · Answer 15 · 2026-04-16 14:01:21

21.8k

Views

Strategies to denest nested radicals $\sqrt{a+b\sqrt{c}}$

Published on 16 Apr 2026 - 14:01

List Question

Combining a radical and simplifying?

Find the limit of: $\lim_{n\to\infty} \frac{1}{\sqrt[n+1]{(n+1)!} - \sqrt[n]{(n)!}}$

How can I calculate this limit: $\lim\limits_{x\rightarrow 2}\frac{2-\sqrt{2+x}}{2^{\frac{1}{3}}-(4-x)^\frac{1}{3}}$?

Limit of a sequence involving root of a factorial: $\lim_{n \to \infty} \frac{n}{ \sqrt [n]{n!}}$

Rationalize and simplify $\frac{x-1}{\sqrt{2\sqrt{x}} + 1 - \sqrt[4]{x}}$

Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational

$\sqrt{x} +y = 4$, $x+ \sqrt{y}= 6$, find the solution $(x,y)$

Range of the solutions for $\sqrt{x} + \sqrt{x+16} = 3$

Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$

Limit (without series expansion and l'Hôpital's rule)

Divergence of the harmonic series and the Cauchy criterion imply $\lim_{n\to\infty} \sqrt[n]n=1$

Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.

Finding $\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$

Limit of quotients with square roots: $\lim_{x\to2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}$

Strategies to denest nested radicals $\sqrt{a+b\sqrt{c}}$

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