List questions from nested-radicals

Published on 26 Jul 2015 - 2:28

288

Views

Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + ...}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.

Published on 28 Jul 2015 - 10:53

502

Views

What is intresting about $\sqrt{\log_x{\exp{\sqrt{\log_x{\exp{\sqrt{\log_x{\exp{\cdots}}}}}}}}}=\log_x{e}$?

Published on 11 Aug 2015 - 1:40

247

Views

Find Solution to an infinite Nested Radicals

Published on 17 Aug 2015 - 17:51

132

Views

Evaluating Continued Product of Radicals

Published on 20 Aug 2015 - 18:43

1.4k

Views

Simplifying Cube Roots Containing a Square Root

Published on 28 Aug 2015 - 10:00

194

Views

What is $\lim_{n\to\infty}2^n\sqrt{2-\sqrt{2+\sqrt{2+\dots+\sqrt{p}}}}$ for $negative$ and other $p$?

Published on 02 Sep 2015 - 15:36

242

Views

Visualizing and understanding $\sqrt{2\sqrt2-1}$

Published on 26 Mar 2026 - 16:04

68

Views

Sum to Infinity-

Published on 10 Sep 2015 - 20:02

413

Views

Find the value of $\sqrt{2+\sqrt{2+\sqrt{2+\dots}} }$

Published on 18 Sep 2015 - 5:19

205

Views

Writing $\sqrt[\large3]2+\sqrt[\large3]4$ with nested roots

Published on 20 Sep 2015 - 21:52

75

Views

Given area of square $= 9+6\sqrt{2}$ Without calculator show its length in form of $(\sqrt{ c}+\sqrt{ d})$

Published on 21 Sep 2015 - 22:47

1.8k

Views

Nested solutions of a quadratic equation.

Published on 28 Mar 2026 - 14:18

64

Views

Rewritting square root of non integer as a recurrence with integral coefficients.

Published on 28 Sep 2015 - 22:38

110

Views

How can I show following sequence of square root is convergent?

Published on 02 Oct 2015 - 23:24

List Question

System of equations to solve this nested radical.

Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + ...}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.

What is intresting about $\sqrt{\log_x{\exp{\sqrt{\log_x{\exp{\sqrt{\log_x{\exp{\cdots}}}}}}}}}=\log_x{e}$?

Find Solution to an infinite Nested Radicals

Evaluating Continued Product of Radicals

Simplifying Cube Roots Containing a Square Root

What is $\lim_{n\to\infty}2^n\sqrt{2-\sqrt{2+\sqrt{2+\dots+\sqrt{p}}}}$ for $negative$ and other $p$?

Visualizing and understanding $\sqrt{2\sqrt2-1}$

Sum to Infinity-

Find the value of $\sqrt{2+\sqrt{2+\sqrt{2+\dots}} }$

Writing $\sqrt[\large3]2+\sqrt[\large3]4$ with nested roots

Given area of square $= 9+6\sqrt{2}$ Without calculator show its length in form of $(\sqrt{ c}+\sqrt{ d})$

Nested solutions of a quadratic equation.

Rewritting square root of non integer as a recurrence with integral coefficients.

How can I show following sequence of square root is convergent?

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