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#1 2016-04-16 04:32:14

evene
Member
Registered: 2015-10-18
Posts: 272

Denesting Nested Radicals Question

So while reading about Nested Radicals on the Wikipedia Page, I came across a problem that said the
can be rewritten as
.


How do you do that? For example: How can you denest the nested radical
?


I'm just a beginner in this. I find it really interesting.

Last edited by evene (2016-04-16 04:40:10)

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#2 2016-04-17 05:04:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Denesting Nested Radicals Question

Hi;

The top one is a Ramanujan identity and there is an algorithm by Susan Landau for denesting but I do not know if it applies to your second radical. It may not be possible to denest the second radical.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-04-17 14:09:30

evene
Member
Registered: 2015-10-18
Posts: 272

Re: Denesting Nested Radicals Question

Apparently, to denest
, you have to assume that it can be simplified into a sum of two surds (radicands). So
.

Last edited by evene (2016-04-17 14:10:05)

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#4 2016-10-16 04:42:58

evene
Member
Registered: 2015-10-18
Posts: 272

Re: Denesting Nested Radicals Question

Going through my old threads, I have decided to answer this question, now that I know how to simplify.

In general, the roots of any cubic equation

can also be written into the form
where
are the roots of the cubic,


and d is the negated discriminant. More specifically,

Last edited by evene (2016-10-16 04:44:11)

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