Yes.
25 - or a little further - is a good first stop.
The reason is that there are another two shortcuts for calculating squares.
For numbers close to 50 you can use:
25 + x | x^2
Where x is the distance from 50.
56^2 = 25 + 6 | 6^2 =
31 | 36 =
3136
66^2 =
25+16 | 16^2 =
41 | 256 =
4356
43^2 =
25 - 7 | 7^2 =
18 | 49 =
1849
See how easy this is?
For numbers close to 100 you can use:
100 + 2x | x^2
where x is the distance from 100.
97^2 = 100 - 2*3 | 3^2 =
94 | 09 =
9409
88^2 =
100-24 | 12^2 =
76 | 144 =
7744
117 ^ 2 =
100 + 2*17 | 17^2 =
134 | 289 =
13689
Again, see how easy this is?
(the notation ‘|’ is a 100’s separator)
So by memorizing the squares up to 25 and these two shortcuts you can easily calculate all squares up to 125:
0-25: memorized.
25-75: 50’s shortcut
75 - 125: 100’s shortcut.
Apart from the soroban, the biggest way to speed up both addition and subtraction is to work with complements more. This turns an addition into a subtracting and vice versa.
89 + 35 = (89 + 11) + (35 - 11) = 124
Think ‘what do I need to get from 89 to 100’.
53 - 27 = (53 + 3) - (27 + 3) = 26
Another way of doing this, is to think ‘from 27 to 30 is 3, then from 30 to 53 is 23’.
If you work this way, there is no carry and this makes the calculation a lot easier.
With 4 or 5 digit numbers , mentally use the | notation and treat it as 2 2-digit numbers:
4958
2789 + = >
49 | 58
27 | 89 +
First do the hundreds:
(49+1 ) + (27-1) = 76
Then the singles:
(58 -11) + (89 + 11) = 147
Then put them together again:
76 | 147 =
7747
5-digit addition:
12345
67890 +
Mentally split into:
1 | 23 | 45
6 | 78 | 90 +
and it out work from left to right.
On the soroban you basically do the same thing.
Instead of adding 80 you add 100 by moving the third bead up and then subtract 20 by shifting 2 second beads down.
The soroban lets you automate this process. After a while your fingers only move beads without even thinking.
On my phone, I use this one:
In a browser, try this: