Question

Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$

score 1k · Answer 1 · 2014-09-26 10:27:42

1k

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Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$

Published on 26 Sep 2014 - 10:27

score 124 · Answer 2 · 2026-03-26 12:42:33

124

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Question analysis so amazing

Published on 26 Mar 2026 - 12:42

score 124 · Answer 3 · 2014-09-27 20:42:05

124

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What is the algebra involved in solving the inequality $\sqrt x\le 2$

Published on 27 Sep 2014 - 20:42

score 4.3k · Answer 4 · 2014-09-27 21:48:18

4.3k

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Finding the integer solutions of the equation $3\sqrt {x + y} + 2\sqrt {8 - x} + \sqrt {6 - y} = 14$

Published on 27 Sep 2014 - 21:48

score 1.4k · Answer 5 · 2014-09-27 22:38:45

1.4k

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Holomorphic branch of the $n^{\mathrm{th}}$ root of $f$

Published on 27 Sep 2014 - 22:38

score 97 · Answer 6 · 2014-09-28 05:47:03

97

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Algebra problem solve for a,b,c and d?

Published on 28 Sep 2014 - 5:47

score 261 · Answer 7 · 2026-03-25 21:22:11

261

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Show that $\sqrt{2}, \sqrt{2+\sqrt{2}}, \sqrt{2+\sqrt{2+\sqrt{2}}},\cdots$

Published on 25 Mar 2026 - 21:22

score 218 · Answer 8 · 2026-03-27 23:32:03

218

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The limit of $\sqrt{x^2+x+1}-\sqrt{x^2+1}$ as $x\to\infty$

Published on 27 Mar 2026 - 23:32

score 446 · Answer 9 · 2026-03-25 11:13:41

446

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Show that $({\sqrt{2}\!+\!1})^{1/n} \!+ ({\sqrt{2}\!-\!1})^{1/n}\!\not\in\mathbb Q$

Published on 25 Mar 2026 - 11:13

score 2.2k · Answer 10 · 2014-09-30 02:01:34

2.2k

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Relationship between Difference of Two Numbers and Their Square Roots

Published on 30 Sep 2014 - 2:01

score 168 · Answer 11 · 2026-03-27 23:40:35

168

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How prove this$\lfloor \sqrt{2x-\lfloor\sqrt{2x}\rfloor}\rfloor=\lfloor\frac{\sqrt{8x+1}-1}{2}\rfloor$

Published on 27 Mar 2026 - 23:40

score 431 · Answer 12 · 2014-09-30 23:40:27

431

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Proving $\lim\limits_{n \to \infty}[\sqrt{n^2 + 1} - n] = 0$

Published on 30 Sep 2014 - 23:40

score 1.9k · Answer 13 · 2026-03-25 09:26:35

1.9k

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Proving that the square root of 5 is irrational

Published on 25 Mar 2026 - 9:26

score 13.3k · Answer 14 · 2026-03-25 21:22:59

13.3k

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Find the value of $\sqrt{10\sqrt{10\sqrt{10...}}}$

Published on 25 Mar 2026 - 21:22

score 305 · Answer 15 · 2026-03-25 21:22:08

305

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Nestedradicals found in the solution of equation $x^{257}=1$

Published on 25 Mar 2026 - 21:22

List Question

Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$

Question analysis so amazing

What is the algebra involved in solving the inequality $\sqrt x\le 2$

Finding the integer solutions of the equation $3\sqrt {x + y} + 2\sqrt {8 - x} + \sqrt {6 - y} = 14$

Holomorphic branch of the $n^{\mathrm{th}}$ root of $f$

Algebra problem solve for a,b,c and d?

Show that $\sqrt{2}, \sqrt{2+\sqrt{2}}, \sqrt{2+\sqrt{2+\sqrt{2}}},\cdots$

The limit of $\sqrt{x^2+x+1}-\sqrt{x^2+1}$ as $x\to\infty$

Show that $({\sqrt{2}\!+\!1})^{1/n} \!+ ({\sqrt{2}\!-\!1})^{1/n}\!\not\in\mathbb Q$

Relationship between Difference of Two Numbers and Their Square Roots

How prove this$\lfloor \sqrt{2x-\lfloor\sqrt{2x}\rfloor}\rfloor=\lfloor\frac{\sqrt{8x+1}-1}{2}\rfloor$

Proving $\lim\limits_{n \to \infty}[\sqrt{n^2 + 1} - n] = 0$

Proving that the square root of 5 is irrational

Find the value of $\sqrt{10\sqrt{10\sqrt{10...}}}$

Nestedradicals found in the solution of equation $x^{257}=1$

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