How to calculate a square root by hand

see also this usenet thread

in decimal

                               | 2
                         1 * 1 | 1
                               | ------------------------------
                               | 100
                        24 * 4 |  96
                               | ------------------------------
                               |  400
                       281 * 1 |  281
                               | ------------------------------
                               |  11900
                      2824 * 4 |  11296
                               | ------------------------------
                               |    60400
                     28282 * 2 |    56564
                               | ------------------------------
                               |     383600
                    282841 * 1 |     282841
                               | ------------------------------
                               |     10075900
                   2828423 * 3 |      8485269
                               | ------------------------------
                               |      159063100
                  28284265 * 5 |      141421325
                               | ------------------------------
                               |       1764177500
                 282842706 * 6 |       1697056236
                               | ------------------------------
                               |         6712126400
                2828427122 * 2 |         5656854244
                               | ------------------------------
                               |         105527215600
               28284271243 * 3 |          84852813729
                               | ------------------------------
                               |          2067440187100
              282842712467 * 7 |          1979898987269
                               | ------------------------------
                               |            8754119983100
             2828427124743 * 3 |            8485281374229
                               | ------------------------------
                               |             26883860887100
            28284271247460 * 0 |                          0
                               | ------------------------------
                               |             2688386088710000
           282842712474609 * 9 |             2545584412271481
                               | ------------------------------
                               |              14280167643851900
          2828427124746185 * 5 |              14142135623730924
                               | ------------------------------
                               |                13803202012097600
         28284271247461900 * 0 |                                0
                               | ------------------------------
                               |                1380320201209760000
        282842712474619004 * 4 |                1131370849898476032
                               | ------------------------------
                               |                 24894935131128397824
       2828427124746190088 * 8 |                 22627416997969518592
                               | ------------------------------
                               |                  226751813315887923200
      28284271247461898248 * 8 |                  226274169979695202304
                               | ------------------------------
                               |                     47764333619272089600
     282842712474619002880 * 0 |                                        0
                               | ------------------------------
                               |                     4776433361927209484288
    2828427124746190192641 * 1 |                     2828427124746190061568
                               | ------------------------------
                               |                     194800623718101942272000
   28284271247461900615686 * 6 |                     169705627484771412082688
                               | ------------------------------
                               |                      2509499623333053018931200
  282842712474619006156808 * 8 |                      2262741699796951982145536
                               | ------------------------------
                               |                       24675792353610103678566400
 2828427124746189977681928 * 8 |                       22627416997969520895197184

>

and in binary

                               | 10
                         1 * 1 |  1
                               | ------------------------------
                               |  100
                       100 * 0 |
                               | ------------------------------
                               |  10000
                      1001 * 1 |   1001
                               | ------------------------------
                               |   11100
                     10101 * 1 |   10101
                               | ------------------------------
                               |     11100
                    101100 * 0 |
                               | ------------------------------
                               |     1110000
                   1011001 * 1 |     1011001
                               | ------------------------------
                               |       1011100
                  10110100 * 0 |
                               | ------------------------------
                               |       101110000
                 101101001 * 1 |       101101001
                               | ------------------------------
                               |             11100
                1011010100 * 0 |
                               | ------------------------------
                               |             1110000
               10110101000 * 0 |
                               | ------------------------------
                               |             111000000
              101101010000 * 0 |
                               | ------------------------------
                               |             11100000000
             1011010100000 * 0 |
                               | ------------------------------
                               |             1110000000000
            10110101000000 * 0 |
                               | ------------------------------
                               |             111000000000000
           101101010000001 * 1 |             101101010000001
                               | ------------------------------
                               |               101010111111100
          1011010100000100 * 0 |
                               | ------------------------------
                               |               10101011111110000
         10110101000001000 * 0 |
                               | ------------------------------
                               |               1010101111111000000
        101101010000010001 * 1 |                101101010000010001
                               | ------------------------------
                               |                10100010111010111100
       1011010100000100101 * 1 |                 1011010100000100101
                               | ------------------------------
                               |                 100100001101001011100
      10110101000001001101 * 1 |                  10110101000001001101
                               | ------------------------------
                               |                   110110010100000111100
     101101010000010011101 * 1 |                   101101010000010011101
                               | ------------------------------
                               |                     100100001111001111100
    1011010100000100111100 * 0 |
                               | ------------------------------
                               |                     10010000111100111110000
   10110101000001001111000 * 0 |
                               | ------------------------------
                               |                     1001000011110011111000000
  101101010000010011110001 * 1 |                      101101010000010011110001
                               | ------------------------------
                               |                       1101100111000101100111100
 1011010100000100111100101 * 1 |                       1011010100000100111100101
                               | ------------------------------
                               |                         1001001100000010101011100