Question

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

score 385 · Answer 1 · 2018-12-14 11:11:17

385

Views

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

Published on 14 Dec 2018 - 11:11

score 422 · Answer 2 · 2019-01-01 19:15:48

422

Views

Does a given infinite nested radical have infinitely many solutions?

Published on 01 Jan 2019 - 19:15

score 1.1k · Answer 3 · 2026-03-25 07:43:49

1.1k

Views

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

Published on 25 Mar 2026 - 7:43

score 69 · Answer 4 · 2026-03-25 01:21:55

69

Views

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

Published on 25 Mar 2026 - 1:21

score 208 · Answer 5 · 2019-01-19 04:24:20

208

Views

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

Published on 19 Jan 2019 - 4:24

score 116 · Answer 6 · 2019-01-19 21:14:02

116

Views

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

Published on 19 Jan 2019 - 21:14

score 131 · Answer 7 · 2019-01-31 00:31:20

131

Views

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

Published on 31 Jan 2019 - 0:31

score 286 · Answer 8 · 2019-01-31 04:53:12

286

Views

Tough Irrational Equation highschool

Published on 31 Jan 2019 - 4:53

score 154 · Answer 9 · 2019-02-04 14:41:00

154

Views

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

Published on 04 Feb 2019 - 14:41

score 172 · Answer 10 · 2019-02-06 22:52:46

172

Views

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

Published on 06 Feb 2019 - 22:52

score 109 · Answer 11 · 2019-02-07 02:22:12

109

Views

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

Published on 07 Feb 2019 - 2:22

score 368 · Answer 12 · 2019-02-17 05:10:18

368

Views

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

Published on 17 Feb 2019 - 5:10

score 5.1k · Answer 13 · 2019-02-20 02:02:55

5.1k

Views

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

Published on 20 Feb 2019 - 2:02

score 235 · Answer 14 · 2019-03-05 16:02:59

235

Views

Infinitely Nested Radical with Fibonacci Coefficients

Published on 05 Mar 2019 - 16:02

score 416 · Answer 15 · 2019-03-11 00:52:27

416

Views

Prove value of $\sin(15°)$

Published on 11 Mar 2019 - 0:52

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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