Sunday, February 7, 2021

TI-86 and DM42/HP42S: Square Root Simplification

TI-86 and DM42/HP42S:  Square Root Simplification


Introduction


The program SQROOT attempts to factor √N into the form A√B (N, A, and B are positive integers).  The program tests whether X^2 evenly divides into N from X = 1 to int(√N).  If successful, let A = X and B = N/X^2.


Example:  


√88   (N = 88)

int(√88) = 9


Test:

88/9^2 ≈ 1.0864

88/8^2 = 1.375

88/7^2 ≈ 1.7959

88/6^2 ≈ 2.4444

88/5^2 = 3.52

88/4^4 = 5.5

88/3^2 ≈ 9.7778

88/2^2 = 22    


2^2 (4) divides into 88 evenly.  


Then A = 2, B = 22.  Therefore √88 = 2√22


TI-86 Program:  SQROOT


*  This code should work on the TI-83/TI-84 Plus family with no or very minor adjustments.


*  The arrow -> is made of two characters:  the minus sign (-) and the greater than sign (>).  


"2021-01-06 EWS"

Disp "√N -> A√B"

Prompt N

iPart(√N)→X

While X≠0

If fPart(N/X^2)==0

Then

X→A 

N/X^2→B

Goto A

Else

X-1→X 

End

End

Lbl A

Disp "√N = A√B : A=", A, "B=" , B



HP 42S/DM42/Free42 Program: SQROOT


*  The character ├ appends (attaches) alpha strings together.  To designate strings to be attached, press ENTER while in ALPHA entry mode.


*  Similarly, pressing RCL while ALPHA mode will allow you to recall the value of a register and attach it to current alpha string.


* The ALL mode is similar to the standard and float mode.


* Registers:  R00 = N, R01 = A, R02 = B


00 {52-Byte Prgm}

01 LBL "SQROOT"

02 "N?"

03 PROMPT

04 STO 00

05 SQRT

06 IP

07 STO 01

08 LBL 00

09 RCL 00

10 RCL 01

11 X↑2

12 ÷

13 STO 02

14 FP

15 X=0?

16 GTO 01

17 1

18 STO- 01

19 GTO 00

20 LBL 01

21 ALL

22 CLA

23 "√"

24 ARCL 00

25 ├"="

26 ARCL 01

27 ├"√"

28 ARCL 02

29 END


Examples


√88 = 2√22


√46 = 1√46


√178 = 1√178


√200 = 10√2


Eddie


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