Question

Prove $\lim_{n \rightarrow \infty} (\sqrt{n^2+1} - n) = 0$ by definition of convergence

score 489 · Answer 1 · 2026-03-31 07:52:59

489

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Prove $\lim_{n \rightarrow \infty} (\sqrt{n^2+1} - n) = 0$ by definition of convergence

Published on 31 Mar 2026 - 7:52

score 346 · Answer 2 · 2026-03-25 01:17:46

346

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number coefficients of an infinite root of 2

Published on 25 Mar 2026 - 1:17

score 97 · Answer 3 · 2016-10-28 03:15:45

97

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Simplifying radical expression $\sqrt[4]{3x}\cdot\sqrt{y+4}$

Published on 28 Oct 2016 - 3:15

score 325 · Answer 4 · 2026-03-30 23:29:03

325

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Simplifying radical expression $\frac{\sqrt{p-4q}}{\sqrt{3q^2+4pq+p^2}}\cdot\frac{\sqrt{p+3q}}{\sqrt{p^2+6pq+8q^2}}\div\frac1{\sqrt{p^2+3pq+2q^2}}$

Published on 30 Mar 2026 - 23:29

score 154 · Answer 5 · 2016-10-29 15:18:56

154

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How can I solve the following question?

Published on 29 Oct 2016 - 15:18

score 248 · Answer 6 · 2026-04-01 14:26:40

248

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How is it possible for a quadratic equation to have one rational root and one irrational root?

Published on 01 Apr 2026 - 14:26

score 72 · Answer 7 · 2026-03-25 04:35:31

72

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Is it inequality true

Published on 25 Mar 2026 - 4:35

score 132 · Answer 8 · 2016-10-30 22:46:26

132

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Finding if sentence is true using induction: $\sqrt1 + \sqrt2 +\dots+\sqrt{n} \le \frac23(n+1)\sqrt{n+1}$

Published on 30 Oct 2016 - 22:46

score 126 · Answer 9 · 2026-03-26 01:23:35

126

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The least positive real number $k$ for which $k\left(\sqrt{(x+y)(y+z)(z+x)}\right)\geq x\sqrt{y}+y\sqrt{z}+z\sqrt{x}$

Published on 26 Mar 2026 - 1:23

score 195 · Answer 10 · 2016-11-01 18:06:13

195

Views

Solve the inequality $\sqrt x+\sqrt{x+1}>\sqrt 3$.

Published on 01 Nov 2016 - 18:06

score 307 · Answer 11 · 2016-11-01 18:51:06

307

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Solve the inequality $\sqrt{(x+2)(x-5)} < 8-x$

Published on 01 Nov 2016 - 18:51

score 84 · Answer 12 · 2016-11-02 07:48:35

84

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Solve the system of equations $\sqrt{x+y}+\sqrt{2x+y+2}=7, 3x+2y=23$.

Published on 02 Nov 2016 - 7:48

score 316 · Answer 13 · 2026-03-25 15:42:21

316

Views

How to prove that $\frac x{\sqrt y}+\frac y{\sqrt x}\ge\sqrt x+\sqrt y$

Published on 25 Mar 2026 - 15:42

score 142 · Answer 14 · 2016-11-03 05:37:27

142

Views

Solving a radical equation

Published on 03 Nov 2016 - 5:37

score 446 · Answer 15 · 2016-11-03 08:28:41

446

Views

Is there a way to get rid of all square roots in an equation with $4$ square roots?

Published on 03 Nov 2016 - 8:28

List Question

Prove $\lim_{n \rightarrow \infty} (\sqrt{n^2+1} - n) = 0$ by definition of convergence

number coefficients of an infinite root of 2

Simplifying radical expression $\sqrt[4]{3x}\cdot\sqrt{y+4}$

Simplifying radical expression $\frac{\sqrt{p-4q}}{\sqrt{3q^2+4pq+p^2}}\cdot\frac{\sqrt{p+3q}}{\sqrt{p^2+6pq+8q^2}}\div\frac1{\sqrt{p^2+3pq+2q^2}}$

How can I solve the following question?

How is it possible for a quadratic equation to have one rational root and one irrational root?

Is it inequality true

Finding if sentence is true using induction: $\sqrt1 + \sqrt2 +\dots+\sqrt{n} \le \frac23(n+1)\sqrt{n+1}$

The least positive real number $k$ for which $k\left(\sqrt{(x+y)(y+z)(z+x)}\right)\geq x\sqrt{y}+y\sqrt{z}+z\sqrt{x}$

Solve the inequality $\sqrt x+\sqrt{x+1}>\sqrt 3$.

Solve the inequality $\sqrt{(x+2)(x-5)} < 8-x$

Solve the system of equations $\sqrt{x+y}+\sqrt{2x+y+2}=7, 3x+2y=23$.

How to prove that $\frac x{\sqrt y}+\frac y{\sqrt x}\ge\sqrt x+\sqrt y$

Solving a radical equation

Is there a way to get rid of all square roots in an equation with $4$ square roots?

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