APB9999 said:
>In school I learned the algorithm for finding square roots by hand. I never used it again. Wish I could remember it, though.
I think I remember the algorithm you’re thinking of. It’s a little reminiscent of long division. Here goes:
To find the square root of 156.25:
place the number under a radical sign (like a long division sign) and group the
digits by two both left and right of the decimal point.
<code>
___.
V 1 56.25
</code>
over the left-most group (the “1” in my example), place the square root of the
largest integer greater than or equal to that group. E.g., a 1 for the groups 1 2 3, a 2 for the groups
4 5 6 7 8, a 3 for 9 10 11 12 13 14 15, etc. Then square this number, place
it under the first group, and subtract.
<code>
1__.__
V 1 56.25
-1
0
</code>
Bring down the next group (“56”) as in long division. To the left of this lowest line,
write double the “quotient” in progress, followed by a blank space.
<code>
1__.__
V 1 56.25
-1
2_ )0 56
</code>
Now comes the tricky part: the “2_” represents twenty-something. Your task is to find a
single digit that will go both above the “56” and next to the 2. Their product will be placed
under the “0 56” and subtracted; it needs to be as large as possible without going over “0 56”. E.g.,
1 * 21 = 21
2 * 22 = 44
3 * 23 = 69 too large
So “2” is the magic digit this round.
<code>
1__2._
V 1 56.25
-1
22 )0 56
-44
12
</code>
Next, bring down the “25” and write a “24_” next to “12 25”
<code>
1__2._
V 1 56.25
-1
22 )0 56
-44
24_ )12 25
</code>
1 * 241 = 241
2 * 242 = 484
3 * 243 = 729
4 * 244 = 976
5 * 245 = 1225 !
<code>
_1__2._5
V 1 56.25
-1
22 )0 56
-44
245 )12 25
12 25
0
</code>
If the subtraction comes out zero, you’ve found an exact answer. If not,
keep bringing down “00” pairs to calculate more places.