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
All original content copyright, © 2011-2021. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
