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#1 2014-07-26 14:55:48

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Square roots


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#2 2014-07-26 19:40:30

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-07-26 20:32:42

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: Square roots

How did you do it? Did you have to solve a fourth degree equation?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#4 2014-07-26 20:34:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

There are a couple of ways to get the answer but first you have a chore to do...


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2014-07-26 20:45:49

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: Square roots

I have a chore?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2014-07-26 20:48:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

Yep, before you can determine the answer which is easy, you must prove convergence.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2014-07-26 21:00:45

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: Square roots

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#8 2014-07-26 21:04:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

There are 2 ways to get the above answer.

1) Solve the equation:

or do some EM.

dummy[] := Block[{}, k = k + 1; (-1)^k]
k = -1; r = 
 Sqrt[Nest[4 + dummy[] Sqrt[#] &, 1, 15]] /. Sqrt[3] -> Sqrt[4];
N[r, 25];
RootApproximant[N[r, 25]] // TraditionalForm

Both ideas require a proof of convergence which though not difficult is harder than the problem itself.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#9 2014-07-27 00:58:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: Square roots

I understand the first solution but I do not know how to solve it by hand.

I do not know what the second solution means


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#10 2014-07-27 01:08:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

How the heck would anyone be expected to solve that by hand?

The second one is M code to do the nested radical.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#11 2014-07-27 01:11:50

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: Square roots

Please  explain the code.

Is the first equation not a proof of convergence itself?

Is there no way to do it by hand?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#12 2014-07-27 01:32:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

I do not think you can handle an equation like that by hand.

The code does this:

run it changing the 15 to a 5.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#13 2014-07-27 01:40:31

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Square roots

Cardano could solve this by hand.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#14 2014-07-27 01:41:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

Is it a fourth degree equation?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#15 2014-07-27 01:49:33

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: Square roots

Your code gives an approximate fraction, bobbym.

Who is Cardino?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#16 2014-07-27 01:51:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Square roots

bobbym wrote:

Is it a fourth degree equation?

Yes, it is.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#17 2014-07-27 01:54:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

Please show it?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#18 2014-07-27 02:02:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Square roots

Hi


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#19 2014-07-27 02:05:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

You got that from this?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#20 2014-07-27 02:05:58

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: Square roots

I've that equation too. How do I solve it by hand?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#21 2014-07-27 02:06:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

I posted an answer to that a while back.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#22 2014-07-27 02:10:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Square roots

bobbym wrote:

You got that from this?

Yep.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#23 2014-07-27 02:11:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

Please show how.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#24 2014-07-27 02:11:54

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,177
Website

Re: Square roots

bobbym wrote:

You got that from this?

Yes


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#25 2014-07-27 02:12:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Square roots

Okay, please show how.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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