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.