January 3rd, 2019, 11:09 PM  #1 
Newbie Joined: Dec 2018 From: syria Posts: 10 Thanks: 0  Square root formulas
I deduced a simpler formula for the square root using only one trigonometric function "acos", it is a controllable precision formula in advance, the correct decimals 2n are controlled by choosing n, based on the discovery of a pattern, the square root is proportional to the angle: √x=1/(10^n acos[x/(x+0.5 10^(2n) )] ) or √x= 10^n x acos[x/(x+0.5 10^(2n) )] Because "acos" is illconditioned I suggest to use a high precision program to calculate the formula such as https://www.wolframalpha.com/ You can check my research paper preprint at : https://www.researchgate.net/profile/Mones_Jaafar I welcome your comments and hope that you find it useful 
January 4th, 2019, 12:53 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,806 Thanks: 716 
Why is this better than usual methods?

January 4th, 2019, 02:17 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra 
what does x/(x+0.5 10^(2n) ) mean? Is it $$\frac{x}{x+0.5 \times 10^{2n}}$$

January 4th, 2019, 03:51 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389  
January 4th, 2019, 10:08 PM  #5 
Newbie Joined: Dec 2018 From: syria Posts: 10 Thanks: 0  You can calculate the square root without iterations or calculations steps, by simply replacing x and choosing n according to your need You can control the correct decimals by simply choosing n if you choose n = 3 you get 2n = 6 correct decimals if you choose n = 18 you get 2n= 36 correct decimals The formulas are based on the discovery of a pattern this is not a calculation method only it is a mathematical law and formulas that illustrate the incontestable relation between the square root and the trigonometric function according to a specific pattern, Thanks, 
January 4th, 2019, 10:12 PM  #6  
Newbie Joined: Dec 2018 From: syria Posts: 10 Thanks: 0  Quote:
to calculate the square root of x choose n that control the correct decimals 2n and calculate the formula using a correct and high precision program such as https://www.wolframalpha.com/  
January 4th, 2019, 10:14 PM  #7 
Newbie Joined: Dec 2018 From: syria Posts: 10 Thanks: 0  
January 4th, 2019, 10:20 PM  #8 
Senior Member Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389  
January 5th, 2019, 01:19 PM  #9  
Global Moderator Joined: May 2007 Posts: 6,806 Thanks: 716  Quote:
 
January 5th, 2019, 03:19 PM  #10 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,257 Thanks: 928 Math Focus: Wibbly wobbly timeywimey stuff.  

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formulas, root, square 
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