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