Math Is Fun Forum

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)

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.
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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)

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)