Question

Show the sequence $\{{\sqrt{5}}~,{\sqrt{5+{\sqrt5}}}~,\sqrt{5+\sqrt{5+\sqrt{5}}}~,...\}$ converges and find its limit.

score 1k · Answer 1 · 2018-04-12 16:49:05

1k

Views

Show the sequence $\{{\sqrt{5}}~,{\sqrt{5+{\sqrt5}}}~,\sqrt{5+\sqrt{5+\sqrt{5}}}~,...\}$ converges and find its limit.

Published on 12 Apr 2018 - 16:49

score 333 · Answer 2 · 2018-04-20 07:28:12

333

Views

Unnesting $\sqrt{1+\sqrt2}$

Published on 20 Apr 2018 - 7:28

score 67 · Answer 3 · 2018-05-24 05:20:56

67

Views

What is the error in this square root denesting?

Published on 24 May 2018 - 5:20

score 160 · Answer 4 · 2018-06-12 17:36:58

160

Views

Simplifying nested radicals with higher-order radicals

Published on 12 Jun 2018 - 17:36

score 102 · Answer 5 · 2026-03-19 23:27:19

102

Views

Do there exist shorter ways of solving for $x$ (or other smarter methods)?

Published on 19 Mar 2026 - 23:27

score 38 · Answer 6 · 2018-06-15 20:20:20

38

Views

Determining rational functions that simplify to a simple expression

Published on 15 Jun 2018 - 20:20

score 254 · Answer 7 · 2018-06-19 10:00:08

254

Views

What is $x$ if $\sqrt{x+4+2\sqrt{x+3}}=\frac{x+8}{3}$?

Published on 19 Jun 2018 - 10:00

score 980 · Answer 8 · 2018-06-26 11:01:09

980

Views

$a+b\sqrt{3}=\sqrt{21-12\sqrt{3}}, a,b \in \mathbb {Z}$ Find a+b

Published on 26 Jun 2018 - 11:01

score 4.9k · Answer 9 · 2018-06-28 05:09:59

4.9k

Views

The value of x satisfying the equation $x=\sqrt{2+\sqrt{2-\sqrt{2+x}}}$

Published on 28 Jun 2018 - 5:09

score 284 · Answer 10 · 2018-07-02 01:59:00

284

Views

How to express $\frac{\frac{1}{2}}{\sqrt[4]{\frac{3}4}-\sqrt[4]{\frac{1}{4}}}$ into $\frac{1}{2}\sqrt{5+3\sqrt{3}+2\sqrt{12+7\sqrt{3}}}$

Published on 02 Jul 2018 - 1:59

score 822 · Answer 11 · 2018-07-03 11:34:34

822

Views

Solving the infinite radical $\sqrt{6+\sqrt{6+2\sqrt{6+3\sqrt{6+...}}}}$

Published on 03 Jul 2018 - 11:34

score 793 · Answer 12 · 2018-07-03 21:03:31

793

Views

Having trouble simplyfing radicals of this sort

Published on 03 Jul 2018 - 21:03

score 2.2k · Answer 13 · 2018-08-01 04:23:37

2.2k

Views

How to simplify $\int{\sqrt[4]{1-8{{x}^{2}}+8{{x}^{4}}-4x\sqrt{{{x}^{2}}-1}+8{{x}^{3}}\sqrt{{{x}^{2}}-1}}dx}$?

Published on 01 Aug 2018 - 4:23

score 2.3k · Answer 14 · 2018-08-13 18:02:54

2.3k

Views

How to prove that $\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}=4$?

Published on 13 Aug 2018 - 18:02

score 166 · Answer 15 · 2018-08-17 13:58:50

166

Views

Show that $3=\sqrt{1+2\sqrt{1+3\sqrt{1+4...}}}$

Published on 17 Aug 2018 - 13:58

List Question

Show the sequence $\{{\sqrt{5}}~,{\sqrt{5+{\sqrt5}}}~,\sqrt{5+\sqrt{5+\sqrt{5}}}~,...\}$ converges and find its limit.

Unnesting $\sqrt{1+\sqrt2}$

What is the error in this square root denesting?

Simplifying nested radicals with higher-order radicals

Do there exist shorter ways of solving for $x$ (or other smarter methods)?

Determining rational functions that simplify to a simple expression

What is $x$ if $\sqrt{x+4+2\sqrt{x+3}}=\frac{x+8}{3}$?

$a+b\sqrt{3}=\sqrt{21-12\sqrt{3}}, a,b \in \mathbb {Z}$ Find a+b

The value of x satisfying the equation $x=\sqrt{2+\sqrt{2-\sqrt{2+x}}}$

How to express $\frac{\frac{1}{2}}{\sqrt[4]{\frac{3}4}-\sqrt[4]{\frac{1}{4}}}$ into $\frac{1}{2}\sqrt{5+3\sqrt{3}+2\sqrt{12+7\sqrt{3}}}$

Solving the infinite radical $\sqrt{6+\sqrt{6+2\sqrt{6+3\sqrt{6+...}}}}$

Having trouble simplyfing radicals of this sort

How to simplify $\int{\sqrt[4]{1-8{{x}^{2}}+8{{x}^{4}}-4x\sqrt{{{x}^{2}}-1}+8{{x}^{3}}\sqrt{{{x}^{2}}-1}}dx}$?

How to prove that $\sqrt[3]{20+14\sqrt{2}}+\sqrt[3]{20-14\sqrt{2}}=4$?

Show that $3=\sqrt{1+2\sqrt{1+3\sqrt{1+4...}}}$

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