Question

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

score 1k · Answer 1 · 2026-04-17 01:33:42

1k

Views

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

Published on 17 Apr 2026 - 1:33

score 336 · Answer 2 · 2026-04-15 11:52:41

336

Views

Unnesting $\sqrt{1+\sqrt2}$

Published on 15 Apr 2026 - 11:52

score 71 · Answer 3 · 2026-04-11 02:00:36

71

Views

What is the error in this square root denesting?

Published on 11 Apr 2026 - 2:00

score 163 · Answer 4 · 2026-04-11 13:30:03

163

Views

Simplifying nested radicals with higher-order radicals

Published on 11 Apr 2026 - 13:30

score 112 · Answer 5 · 2026-04-30 20:10:36

112

Views

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

Published on 30 Apr 2026 - 20:10

score 43 · Answer 6 · 2026-04-17 04:29:01

43

Views

Determining rational functions that simplify to a simple expression

Published on 17 Apr 2026 - 4:29

score 257 · Answer 7 · 2026-04-16 07:49:35

257

Views

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

Published on 16 Apr 2026 - 7:49

score 983 · Answer 8 · 2026-04-16 06:54:47

983

Views

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

Published on 16 Apr 2026 - 6:54

score 4.9k · Answer 9 · 2026-04-16 14:31:33

4.9k

Views

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

Published on 16 Apr 2026 - 14:31

score 287 · Answer 10 · 2026-04-17 01:50:27

287

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 17 Apr 2026 - 1:50

score 825 · Answer 11 · 2026-04-16 20:06:29

825

Views

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

Published on 16 Apr 2026 - 20:06

score 796 · Answer 12 · 2026-04-15 12:42:01

796

Views

Having trouble simplyfing radicals of this sort

Published on 15 Apr 2026 - 12:42

score 2.2k · Answer 13 · 2026-04-15 21:01:12

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 15 Apr 2026 - 21:01

score 2.3k · Answer 14 · 2026-04-15 16:08:24

2.3k

Views

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

Published on 15 Apr 2026 - 16:08

score 169 · Answer 15 · 2026-04-15 23:56:16

169

Views

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

Published on 15 Apr 2026 - 23:56

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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