The root of a number?

[d]

Does anybody know how you work out a number to the 15th root, only using
add, subtract, multiply and divide?

[math...@hotmail.com]

In article <3607a...@stan.astra.co.uk>,

"d" <Dan...@netbase.co.uk> wrote:
> Does anybody know how you work out a number to the 15th root, only using
> add, subtract, multiply and divide?
>
>

No.

-----== Posted via Deja News, The Leader in Internet Discussion ==-----
http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum

[Dave Astles]

It cannot be done (it is in general impossible, not that nobody knows how to
do it).

There are nevertheless algorithms which can perform the calculation to
arbitrary accuracy.

d wrote in message <3607a...@stan.astra.co.uk>...

[Tom Crispin]

To find p root(a).

Estimate an answer and call this u[1]
A better estimate is (1/p){(p-1)(u[n] + (a/{u[n]^(p-1)})}

--
Best wishes, Tom.
Veni Vidi Bibi
tom_c...@msn.com

[Tom Crispin]

To find the 15th root of a:

Estimate an answer and call this u[1]

A better estimate is (1/15){14u[n] + a/(u[n]^14)}
Repeat the above until you have a sufficiently accurate value of 15 root(a)

[Jeremy Boden]

In article <6u8s8p$bh0$1...@nnrp1.dejanews.com>, math...@hotmail.com
writes

>In article <3607a...@stan.astra.co.uk>,
> "d" <Dan...@netbase.co.uk> wrote:

>> Does anybody know how you work out a number to the 15th root, only using
>> add, subtract, multiply and divide?
>>
>>

> No.
>
>-----== Posted via Deja News, The Leader in Internet Discussion ==-----
>http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum

I do!

Try Newton-Raphson method.

--
Jeremy Boden

[math...@hotmail.com]

In article <5HBrtJA$dCC2...@jboden.demon.co.uk>,

Jeremy Boden <jer...@jboden.demon.co.uk> wrote:
> In article <6u8s8p$bh0$1...@nnrp1.dejanews.com>, math...@hotmail.com
> writes
> >In article <3607a...@stan.astra.co.uk>,
> > "d" <Dan...@netbase.co.uk> wrote:
> >> Does anybody know how you work out a number to the 15th root, only using
> >> add, subtract, multiply and divide?
> >>
> >>
> > No.
> >
>

> I do!
>
> Try Newton-Raphson method.
>
> --
> Jeremy Boden

*************************
This does not give the root ---only successive approximations.
And, his question specifically allowed only addition, subtraction,
multiplication and division---differentiation was not included!

[Jeremy Boden]

In article <6uathi$e0b$1...@nnrp1.dejanews.com>, math...@hotmail.com

writes
>In article <5HBrtJA$dCC2...@jboden.demon.co.uk>,
> Jeremy Boden <jer...@jboden.demon.co.uk> wrote:
>> In article <6u8s8p$bh0$1...@nnrp1.dejanews.com>, math...@hotmail.com
>> writes
>> >In article <3607a...@stan.astra.co.uk>,
>> > "d" <Dan...@netbase.co.uk> wrote:
>> >> Does anybody know how you work out a number to the 15th root, only using
>> >> add, subtract, multiply and divide?
>> >>
>> >>
>> > No.
>> >
>>
>> I do!
>>
>> Try Newton-Raphson method.
>>
>> --
>> Jeremy Boden
>*************************
> This does not give the root ---only successive approximations.
>And, his question specifically allowed only addition, subtraction,
>multiplication and division---differentiation was not included!
>
>-----== Posted via Deja News, The Leader in Internet Discussion ==-----
>http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum

But the differentiation is according to a standard style and so is part
of the basic method. No requirement for a *finite* method was imposed.

--
Jeremy Boden

[robin motz]

You can always do (1) by deMoivre's theorem (via Euler). If
e^((2)(pi)(i)) = 1, then the 15th roots of 1 are given by
e^((2)(pi)(i)/15, and cycling the argument by 2pi fifteen times, and
using e^(ix) = cos(x) + i sin(x), so the first root is cos (360/15) + i
sin (360/15) ,etc. Of course, for the other integers, life is much more
complicated.