List questions from nested-radicals

Published on 03 Aug 2017 - 12:36

136

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Where is the lost root?

Published on 11 Aug 2017 - 21:26

310

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Find $x\in \Bbb Z$ such that $x=\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}$

Published on 30 Mar 2026 - 3:56

236

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$\sqrt[3]{8\div{\sqrt[3]{8\div{\sqrt[3]{8\div{\sqrt[3]{8\div ...} }} }} }} $=?

Published on 16 Aug 2017 - 4:19

360

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Simplify $\sqrt{6-\sqrt{20}}$

Published on 20 Aug 2017 - 15:59

155

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$\sqrt[7]{3+\sqrt[7]{3+\sqrt[7]{3+\dotso}}}$

Published on 21 Aug 2017 - 9:04

200

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Proving $\sqrt{3+\sqrt{13+4\sqrt{3}}} = 1+\sqrt{3}$.

Published on 25 Aug 2017 - 12:16

1.2k

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Solve $ \int_0^2 \sqrt{x+\sqrt{x+\sqrt{x+\dotsb}}}\,dx $

Published on 01 Sep 2017 - 2:41

1.8k

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Find the square root of $14+6\sqrt5 $

Published on 02 Sep 2017 - 6:57

98

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Simplify a square root in another square root

Published on 18 Sep 2017 - 3:41

135

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Prove that $m = \sqrt {n +\sqrt {n +\sqrt {n + \cdots}}}$ is an integer if and only if $n$ is equal to twice a triangular number.

Published on 18 Sep 2017 - 18:17

690

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Simplify $\sqrt{3+\sqrt{8}}$

Published on 19 Sep 2017 - 10:59

403

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A Ramanujan-type trigonometric identity

Published on 21 Sep 2017 - 22:28

5.6k

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Why is $\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3$?

Published on 23 Sep 2017 - 16:41

443

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Are there any known criteria in order for $\sqrt{a_1+\sqrt{a_2-\sqrt{a_3+\sqrt{a_4-\sqrt{a_5+\ldots}}}}}$ to converge?

Published on 28 Sep 2017 - 23:05

List Question

Ramanujan's Infinite Root

Where is the lost root?

Find $x\in \Bbb Z$ such that $x=\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}$

$\sqrt[3]{8\div{\sqrt[3]{8\div{\sqrt[3]{8\div{\sqrt[3]{8\div ...} }} }} }} $=?

Simplify $\sqrt{6-\sqrt{20}}$

$\sqrt[7]{3+\sqrt[7]{3+\sqrt[7]{3+\dotso}}}$

Proving $\sqrt{3+\sqrt{13+4\sqrt{3}}} = 1+\sqrt{3}$.

Solve $ \int_0^2 \sqrt{x+\sqrt{x+\sqrt{x+\dotsb}}}\,dx $

Find the square root of $14+6\sqrt5 $

Simplify a square root in another square root

Prove that $m = \sqrt {n +\sqrt {n +\sqrt {n + \cdots}}}$ is an integer if and only if $n$ is equal to twice a triangular number.

Simplify $\sqrt{3+\sqrt{8}}$

A Ramanujan-type trigonometric identity

Why is $\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3$?

Are there any known criteria in order for $\sqrt{a_1+\sqrt{a_2-\sqrt{a_3+\sqrt{a_4-\sqrt{a_5+\ldots}}}}}$ to converge?

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