List questions from nested-radicals

Published on 25 Dec 2014 - 23:40

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Calculate $\sqrt{\frac{1}{2}} \times \sqrt{\frac{1}{2} + \frac{1}{2}\sqrt{\frac{1}{2}}} \times \ldots $

Published on 26 Dec 2014 - 15:44

345

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Ramanujan's Nested Radical

Published on 06 Oct 2019 - 5:11

76

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Solution to complicated expression with nested radicals

Published on 13 Oct 2019 - 0:02

258

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Closed form for $\sqrt{1+\sqrt{x+\sqrt{x^2+\sqrt{x^3+\sqrt{x^4+...}}}}}$

Published on 17 Oct 2019 - 1:08

501

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More infinite nested square roots

Published on 18 Oct 2019 - 3:48

61

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Nested square root for random variables

Published on 19 Oct 2019 - 16:53

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If $\sqrt{27-10\sqrt{2}} = a+b$, where $a$ is a positive integer and $b$ is between $0$ and $1$, what is $\frac{a+b}{a-b}$?

Published on 19 Oct 2019 - 23:11

302

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Ramanujan's Nested Radicals: evaluating $\sqrt{4+\sqrt{16+\sqrt{64+\sqrt{\cdots}}}}$

Published on 20 Oct 2019 - 1:42

493

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The sum of infinite fours: $\sqrt{4^0+\sqrt{4^1+ \sqrt{4^2+ \dots}}}=?$

Published on 21 Oct 2019 - 7:52

330

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Is there a general identity for the infinite radicals; $\sqrt{n^{0}+\sqrt{n^{1}+\sqrt{n^{2}+\sqrt{n^{3}+...}}}}$

Published on 24 Oct 2019 - 10:27

182

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Division of 2 different Infinite Nested square roots

Published on 03 Nov 2019 - 18:02

235

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What is $\sqrt{i^0+\sqrt{i^1+\sqrt{i^2+...}}}$

Published on 19 Nov 2019 - 17:04

43

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Reduce the radical

Published on 21 Nov 2019 - 20:52

77

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About $\sqrt[k]{l + \sqrt[k]{l + \sqrt[k]{l + ...}}} $ asymptotics

Published on 25 Mar 2026 - 18:08

List Question

Simplifying $\sqrt {1+\sqrt 5}$

Calculate $\sqrt{\frac{1}{2}} \times \sqrt{\frac{1}{2} + \frac{1}{2}\sqrt{\frac{1}{2}}} \times \ldots $

Ramanujan's Nested Radical

Solution to complicated expression with nested radicals

Closed form for $\sqrt{1+\sqrt{x+\sqrt{x^2+\sqrt{x^3+\sqrt{x^4+...}}}}}$

More infinite nested square roots

Nested square root for random variables

If $\sqrt{27-10\sqrt{2}} = a+b$, where $a$ is a positive integer and $b$ is between $0$ and $1$, what is $\frac{a+b}{a-b}$?

Ramanujan's Nested Radicals: evaluating $\sqrt{4+\sqrt{16+\sqrt{64+\sqrt{\cdots}}}}$

The sum of infinite fours: $\sqrt{4^0+\sqrt{4^1+ \sqrt{4^2+ \dots}}}=?$

Is there a general identity for the infinite radicals; $\sqrt{n^{0}+\sqrt{n^{1}+\sqrt{n^{2}+\sqrt{n^{3}+...}}}}$

Division of 2 different Infinite Nested square roots

What is $\sqrt{i^0+\sqrt{i^1+\sqrt{i^2+...}}}$

Reduce the radical

About $\sqrt[k]{l + \sqrt[k]{l + \sqrt[k]{l + ...}}} $ asymptotics

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