Question

How to evaluate $\lim_{x \to \infty}\left(\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}\right)$?

score 332 · Answer 1 · 2026-03-30 03:02:06

332

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How to evaluate $\lim_{x \to \infty}\left(\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}\right)$?

Published on 30 Mar 2026 - 3:02

score 13.4k · Answer 2 · 2013-05-17 20:44:36

13.4k

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Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$

Published on 17 May 2013 - 20:44

score 292 · Answer 3 · 2026-04-08 17:29:09

292

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Proving that $\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{100}}<20$

Published on 08 Apr 2026 - 17:29

score 1.7k · Answer 4 · 2026-03-30 03:00:32

1.7k

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How to evaluate $\sqrt[3]{a + ib} + \sqrt[3]{a - ib}$?

Published on 30 Mar 2026 - 3:00

score 1.2k · Answer 5 · 2013-05-22 12:56:52

1.2k

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Solve equations $\sqrt{t +9} - \sqrt{t} = 1$

Published on 22 May 2013 - 12:56

score 1.5k · Answer 6 · 2026-04-04 00:35:35

1.5k

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Is it possible to rationalize a denominator containing two cube roots?

Published on 04 Apr 2026 - 0:35

score 1.7k · Answer 7 · 2013-05-26 14:50:35

1.7k

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When does $\sqrt{wz}=\sqrt{w}\sqrt{z}$?

Published on 26 May 2013 - 14:50

score 774 · Answer 8 · 2013-05-29 02:46:14

774

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Simplifying a radical equation?

Published on 29 May 2013 - 2:46

score 2.4k · Answer 9 · 2013-05-31 22:40:39

2.4k

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The limit $\lim\limits_{n\to\infty} (\sqrt{n^2-n}-n)$. Algebraic and intuitive thoughts.

Published on 31 May 2013 - 22:40

score 24.7k · Answer 10 · 2013-06-01 02:51:08

24.7k

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How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?

Published on 01 Jun 2013 - 2:51

score 208 · Answer 11 · 2013-06-08 19:10:04

208

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Estimating the nested radical with $1,2,3,4,\dots$ under square root signs

Published on 08 Jun 2013 - 19:10

score 3.8k · Answer 12 · 2013-06-09 20:34:29

3.8k

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The limit of $\lim\limits_{x \to \infty}\sqrt{x^2+3x-4}-x$

Published on 09 Jun 2013 - 20:34

score 374 · Answer 13 · 2013-06-11 22:21:25

374

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Evaluating $\lim\limits_{x\to1}\frac{\sqrt[3]{x^3+1}}{\sqrt[3]{x+1}}$?

Published on 11 Jun 2013 - 22:21

score 923 · Answer 14 · 2013-06-12 20:54:58

923

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$\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_n} = L$ implies $\lim_{n\rightarrow\infty}a_n^{1/n}=L$

Published on 12 Jun 2013 - 20:54

score 22.2k · Answer 15 · 2013-06-17 07:31:34

22.2k

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What is $\sum\limits_{i=1}^n \sqrt i\ $?

Published on 17 Jun 2013 - 7:31

List Question

How to evaluate $\lim_{x \to \infty}\left(\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}\right)$?

Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$

Proving that $\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{100}}<20$

How to evaluate $\sqrt[3]{a + ib} + \sqrt[3]{a - ib}$?

Solve equations $\sqrt{t +9} - \sqrt{t} = 1$

Is it possible to rationalize a denominator containing two cube roots?

When does $\sqrt{wz}=\sqrt{w}\sqrt{z}$?

Simplifying a radical equation?

The limit $\lim\limits_{n\to\infty} (\sqrt{n^2-n}-n)$. Algebraic and intuitive thoughts.

How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?

Estimating the nested radical with $1,2,3,4,\dots$ under square root signs

The limit of $\lim\limits_{x \to \infty}\sqrt{x^2+3x-4}-x$

Evaluating $\lim\limits_{x\to1}\frac{\sqrt[3]{x^3+1}}{\sqrt[3]{x+1}}$?

$\lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_n} = L$ implies $\lim_{n\rightarrow\infty}a_n^{1/n}=L$

What is $\sum\limits_{i=1}^n \sqrt i\ $?

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