Question

How would you prove $\int^8_0\frac1{\sqrt{x+\frac1{\sqrt{x}}}}dx<4-\frac1{2019}$?

score 388 · Answer 1 · 2026-04-14 17:57:20

388

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How would you prove $\int^8_0\frac1{\sqrt{x+\frac1{\sqrt{x}}}}dx<4-\frac1{2019}$?

Published on 14 Apr 2026 - 17:57

score 425 · Answer 2 · 2026-04-10 20:08:19

425

Views

Does a given infinite nested radical have infinitely many solutions?

Published on 10 Apr 2026 - 20:08

score 1.1k · Answer 3 · 2026-05-10 15:00:09

1.1k

Views

Show that the maximum value of this nested radical is $\phi-1$

Published on 10 May 2026 - 15:00

score 72 · Answer 4 · 2026-05-10 14:04:30

72

Views

Is there a nice algorithm for testing the equality of two nested radicals?

Published on 10 May 2026 - 14:04

score 211 · Answer 5 · 2026-04-15 20:07:16

211

Views

Solving $\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}$

Published on 15 Apr 2026 - 20:07

score 117 · Answer 6 · 2026-03-25 09:29:14

117

Views

What is the minimum value of $f_\infty=\frac{x}{\sqrt{x-\sqrt[3]{x-\sqrt[4]{x-\cdots}}}}$?

Published on 25 Mar 2026 - 9:29

score 134 · Answer 7 · 2026-04-16 02:46:56

134

Views

Is it guaranteed that $\sqrt[3]{a+\sqrt{b}}$ can be denested?

Published on 16 Apr 2026 - 2:46

score 290 · Answer 8 · 2026-04-10 07:54:07

290

Views

Tough Irrational Equation highschool

Published on 10 Apr 2026 - 7:54

score 157 · Answer 9 · 2026-04-17 09:58:36

157

Views

Find rational numbers $\alpha $ and $\beta$ in $\sqrt[3]{7+5\sqrt{2}}=\alpha+\beta\sqrt{2}$

Published on 17 Apr 2026 - 9:58

score 175 · Answer 10 · 2026-04-12 13:51:16

175

Views

How do I simplify $\sqrt {4(2- \sqrt{3})}$ into $\sqrt{6} - \sqrt{2}$

Published on 12 Apr 2026 - 13:51

score 112 · Answer 11 · 2026-04-14 01:51:07

112

Views

How can I simplify $\sqrt{\frac{5+\sqrt{5}}{2}}$?

Published on 14 Apr 2026 - 1:51

score 371 · Answer 12 · 2026-04-17 13:44:43

371

Views

Prove that inequality $\sqrt{2\sqrt{4\sqrt{8....\sqrt{2^n}}}} \leqslant n+1$

Published on 17 Apr 2026 - 13:44

score 5.1k · Answer 13 · 2026-04-12 21:35:50

5.1k

Views

Ramanujan's radical and how we define an infinite nested radical

Published on 12 Apr 2026 - 21:35

score 238 · Answer 14 · 2026-04-11 17:38:08

238

Views

Infinitely Nested Radical with Fibonacci Coefficients

Published on 11 Apr 2026 - 17:38

score 419 · Answer 15 · 2026-04-11 20:27:51

419

Views

Prove value of $\sin(15°)$

Published on 11 Apr 2026 - 20:27

List Question

How would you prove $\int^8_0\frac1{\sqrt{x+\frac1{\sqrt{x}}}}dx<4-\frac1{2019}$?

Does a given infinite nested radical have infinitely many solutions?

Show that the maximum value of this nested radical is $\phi-1$

Is there a nice algorithm for testing the equality of two nested radicals?

Solving $\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}$

What is the minimum value of $f_\infty=\frac{x}{\sqrt{x-\sqrt[3]{x-\sqrt[4]{x-\cdots}}}}$?

Is it guaranteed that $\sqrt[3]{a+\sqrt{b}}$ can be denested?

Tough Irrational Equation highschool

Find rational numbers $\alpha $ and $\beta$ in $\sqrt[3]{7+5\sqrt{2}}=\alpha+\beta\sqrt{2}$

How do I simplify $\sqrt {4(2- \sqrt{3})}$ into $\sqrt{6} - \sqrt{2}$

How can I simplify $\sqrt{\frac{5+\sqrt{5}}{2}}$?

Prove that inequality $\sqrt{2\sqrt{4\sqrt{8....\sqrt{2^n}}}} \leqslant n+1$

Ramanujan's radical and how we define an infinite nested radical

Infinitely Nested Radical with Fibonacci Coefficients

Prove value of $\sin(15°)$

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