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Topic: sqrt(x) without approximation?
Replies: 17   Last Post: Nov 6, 2015 8:05 PM

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Posts: 1,448
Registered: 4/7/12
Re: sqrt(x) without approximation?
Posted: Feb 10, 2013 2:46 AM
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On 10 Feb, 00:32, wrote:
> On Saturday, February 9, 2013 1:30:25 PM UTC-8, Virgil wrote:
> > In article
> > <>,
> >  JT <> wrote:

> > > Is there always such a base for any N that we can write sqrt(N)
> > > without approximation? Would it matter if we use NyaN or standard
> > > bases.

> > No and no!
> > While sqrt(N) for nonsquare N, can be approximated in standard
> > notations, I do not see that there can be any analog to digits to the
> > right of a decimal point for your NyaN numbers.

> In base sqrt(n), n is expressed as 100.  I'm not sure how to add the
> natural number 1 to a number in a fractional base system where the
> base is > 1.  I would presume that in base 2.5(decimal), 2 + 1 = 10.111...,
> though I'm not quite sure.

What base are you writing 2,5 equal 10.111... you totally lost me
here, can you write out the multiples so i see what is going on?
Since number systems is represenational you can write any decimal on
the form 0,000512 =10^-6*512 this is also true for anybase, so if we
want to write 2,5 in ternary it will be 2,12 since 12 = 5 =1*3+2*1 in
And we can use this fact for anybase as long we keep track of the
positional multiple. Ternary base 1,3,9,27,81 and so on.

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