Question

simplify 2$\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}$

score 1.5k · Answer 1 · 2026-04-16 12:51:31

1.5k

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simplify 2$\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}$

Published on 16 Apr 2026 - 12:51

score 710 · Answer 2 · 2026-04-16 05:17:27

710

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Evaluating $Q = \sqrt{1!+\sqrt{2!+\sqrt{3!+\dots}}}$

Published on 16 Apr 2026 - 5:17

score 63 · Answer 3 · 2026-04-15 10:41:13

63

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Reference request: infinitely nested radicals.

Published on 15 Apr 2026 - 10:41

score 101 · Answer 4 · 2026-03-26 14:41:39

101

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Does Khinchin's constant have an analog for nested radicals?

Published on 26 Mar 2026 - 14:41

score 259 · Answer 5 · 2026-04-16 21:44:02

259

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Is there a closed form for $3\cdot\frac{3}{\sqrt{6}}\cdot\frac{3}{\sqrt{6+\sqrt{6}}}\cdot\frac{3}{\sqrt{6+\sqrt{6+\sqrt{6}}}}\cdots$?

Published on 16 Apr 2026 - 21:44

score 59 · Answer 6 · 2026-04-14 09:58:01

59

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Denest $\sqrt{3+\sin\frac{\pi}{4}-4\cos\frac{\pi}{8}}$ in terms of possible trigonometric functions.

Published on 14 Apr 2026 - 9:58

score 106 · Answer 7 · 2026-04-12 18:25:24

106

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Nested radical of Ramanujan and cyclic inequality

Published on 12 Apr 2026 - 18:25

score 218 · Answer 8 · 2026-04-13 11:22:20

218

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Nested radical and rationality

Published on 13 Apr 2026 - 11:22

score 138 · Answer 9 · 2026-04-19 03:13:02

138

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How to prove that $\sqrt{1+\frac{1}{2}\sqrt{1+\frac{1}{3}\sqrt{1+\frac{1}{4}\sqrt{\cdots}}}}<\sqrt[3] 2$

Published on 19 Apr 2026 - 3:13

score 126 · Answer 10 · 2026-03-25 23:42:41

126

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Show $\frac{\sqrt{\sqrt[4]8-\sqrt{\sqrt2+1}\;}}{\sqrt{\sqrt[4]8+\sqrt{\sqrt2-1}\;} -\sqrt{\sqrt[4]8-\sqrt{\sqrt2-1}\;}}=\frac1{\sqrt2}$

Published on 25 Mar 2026 - 23:42

score 106 · Answer 11 · 2026-04-13 08:05:09

106

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Infinite complex nested radical and it's complex conjugate.

Published on 13 Apr 2026 - 8:05

score 529 · Answer 12 · 2026-04-16 00:41:22

529

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Prove that $\sqrt[3]{18 + \sqrt{325}} + \sqrt[3]{18 - \sqrt{325}} = 3$ without using Cardano's formula. (Hint, what is $(3\pm \sqrt{13})^3$

Published on 16 Apr 2026 - 0:41

score 129 · Answer 13 · 2026-04-14 02:55:37

129

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Denesting $\sqrt{20+ \sqrt{96}+\sqrt{12}}$ into four possible radicals

Published on 14 Apr 2026 - 2:55

score 177 · Answer 14 · 2026-04-14 17:53:06

177

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Minimal polynomial of $\sqrt{3+2\sqrt{3}}$

Published on 14 Apr 2026 - 17:53

score 161 · Answer 15 · 2026-04-08 21:27:25

161

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Value of $\sqrt{\sum_{k=1}^{1}k+\sqrt{\sum_{k=1}^{2}k+\sqrt{\sum_{k=1}^{3}k...}}}$

Published on 08 Apr 2026 - 21:27

List Question

simplify 2$\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}$

Evaluating $Q = \sqrt{1!+\sqrt{2!+\sqrt{3!+\dots}}}$

Reference request: infinitely nested radicals.

Does Khinchin's constant have an analog for nested radicals?

Is there a closed form for $3\cdot\frac{3}{\sqrt{6}}\cdot\frac{3}{\sqrt{6+\sqrt{6}}}\cdot\frac{3}{\sqrt{6+\sqrt{6+\sqrt{6}}}}\cdots$?

Denest $\sqrt{3+\sin\frac{\pi}{4}-4\cos\frac{\pi}{8}}$ in terms of possible trigonometric functions.

Nested radical of Ramanujan and cyclic inequality

Nested radical and rationality

How to prove that $\sqrt{1+\frac{1}{2}\sqrt{1+\frac{1}{3}\sqrt{1+\frac{1}{4}\sqrt{\cdots}}}}<\sqrt[3] 2$

Show $\frac{\sqrt{\sqrt[4]8-\sqrt{\sqrt2+1}\;}}{\sqrt{\sqrt[4]8+\sqrt{\sqrt2-1}\;} -\sqrt{\sqrt[4]8-\sqrt{\sqrt2-1}\;}}=\frac1{\sqrt2}$

Infinite complex nested radical and it's complex conjugate.

Prove that $\sqrt[3]{18 + \sqrt{325}} + \sqrt[3]{18 - \sqrt{325}} = 3$ without using Cardano's formula. (Hint, what is $(3\pm \sqrt{13})^3$

Denesting $\sqrt{20+ \sqrt{96}+\sqrt{12}}$ into four possible radicals

Minimal polynomial of $\sqrt{3+2\sqrt{3}}$

Value of $\sqrt{\sum_{k=1}^{1}k+\sqrt{\sum_{k=1}^{2}k+\sqrt{\sum_{k=1}^{3}k...}}}$

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