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Anonymous Tue 15 Feb 16:22:54 2022 No.14231972 View Reply Original Report

Quoted By: >>14231976 >>14232016 >>14233763

Why do square roots have really long sequences?

Anonymous

Anonymous Tue 15 Feb 2022 16:25:16 No.14231976 Report

Quoted By: >>14231991

>>14231972
Wut

Anonymous

Anonymous Tue 15 Feb 2022 16:29:40 No.14231991 Report

Quoted By: >>14232061

>>14231976
Why do square root of non square numbers have really long decimal sequences?

Anonymous

Anonymous Tue 15 Feb 2022 16:37:35 No.14232016 Report

Quoted By:

>>14231972
The answer is simple. By use of Laplace's method on the gamma function One arrives at the fact that the square root of n can be approximated as n!*(e/n)^n*1/sqrt(2pi). Now e and pi are irrational which implies the square root of n can be approximated really well by an irrational number.

Anonymous

Anonymous Tue 15 Feb 2022 16:43:00 No.14232033 Report

Quoted By:

All numbers have really long sequences of decimals.
1 = .999...
2 = 1.999...
.5 = .4999...

And so forth. We only choose to ignore the last bit because most of mathematics doesn't need it save for some areas of analysis, unless you're inside the hyperreals of course.

Anonymous

Anonymous Tue 15 Feb 2022 16:51:58 No.14232061 Report

Quoted By: >>14232086 >>14233777

>>14231991
Suppose the square root of a prime number was not a 'really long sequence'.

$\frac{x}{y} = \sqrt{n}$
$\frac{x^2}{y^2} = n$
We can assume that x and y are at least relatively prime to each other.
$x^2 = n*y^2$
We see that $x^2$ must contain the factor n, therefore $x^2 = n^2z^2$ .
Similar argument will lead to $y^2 = n^2a^2$ , therefore x,y were not relatively prime to each other as we assumed before.

Anonymous

Anonymous Tue 15 Feb 2022 16:59:51 No.14232086 Report

Quoted By: >>14233752

>>14232061
n... what does n mean? Like nth term? Or is that representing a sequence?

Anonymous

Anonymous Wed 16 Feb 2022 01:56:57 No.14233752 Report

Quoted By:

>>14232086
it represents that you're n idiot

Anonymous

Anonymous Wed 16 Feb 2022 01:59:45 No.14233763 Report

Quoted By:

>>14231972
because R is infinitely bigger than Q and you have the really small probability to get a rational number taking square root from a random number.

Anonymous

Anonymous Wed 16 Feb 2022 02:03:53 No.14233777 Report

Quoted By:

>>14232061
Huh? Are you implying that a^2/b^2 is the same as (a/b)^2?

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