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(12C) Square Root
10-02-2019, 10:23 AM (This post was last modified: 10-03-2019 04:10 AM by Gamo.)
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(12C) Square Root
For case study purpose here is the very interesting algorithm to compute the square root of a number
by using this equation.

B = [A+(n÷A)] ÷ 2

This equation used Successive Approximation Algorithms that continue to better approximate some desired result by providing the initial guess then this program will converge on to the correct answer if your initial guess is bad then more iteration will be required to achieve a giving accuracy.
With this program it doesn't matter where you start your initial guess because this algorithm also used the
Change in the Approximation: ABS [(B-A) ÷ A] and Tolerance of 0.00000001 to guarantee that the result will be possible.

This equation solves for B, which is the new improved approximation for the square root of n until we are happy with this approximation, we continue repeating the process by coping the new B value into A and then re-executing the same equation to get a new B value.
-----------------------------------
Procedure: FIX 8
n [ENTER] A [R/S] display Answer [X<>Y] number of iterations
-----------------------------------
Example: √10 used 3 as a guess

10 [ENTER] 3 [R/S] 3.16227766 [X<>Y] 3.00000000

Answer: √10 = 3.16227766 and program took 3 iterations to get this answer.
------------------------------------
Program:
Code:

01 STO 2  // A
02 R↓
03 STO 1  // n
04  0
05 STO 0  // Counter 
06 RCL 1  
07 RCL 2  
08  ÷   
09 LSTx  
10  +
11  2
12  ÷ 
13 STO 3  // Store B
14 RCL 2
15  -
16 LSTx
17  ÷
18  0
19 X<>Y
20 X≤Y
21 CHS
22 EEX
23 CHS
24  8
25 X<>Y
26 X≤Y
27 GTO 33
28 RCL 3  // B
29 STO 2  // Store A
30  1
31 STO+0
32 GTO 06
33 RCL 0
34 RCL 3
35 GTO 00

Gamo
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Messages In This Thread
(12C) Square Root - Gamo - 10-02-2019 10:23 AM
RE: (12C) Square Root - Albert Chan - 10-02-2019, 02:36 PM
RE: (12C) Square Root - Albert Chan - 09-28-2020, 05:18 PM
RE: (12C) Square Root - Albert Chan - 09-28-2020, 07:14 PM
RE: (12C) Square Root - Gamo - 10-03-2019, 02:01 AM
RE: (12C) Square Root - SlideRule - 09-28-2020, 09:45 PM
RE: (12C) Square Root - Albert Chan - 06-08-2021, 03:36 PM
RE: (12C) Square Root - depor - 12-21-2023, 11:50 PM
RE: (12C) Square Root - Dave Hicks - 12-23-2023, 01:48 AM
RE: (12C) Square Root - Thomas Klemm - 12-23-2023, 04:26 AM



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