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Explain the process of square root by division method.
Square Root by Division method
Let us understand with an example: 46655
First, divide the number to be square-rooted into pairs of digits, starting at the decimal point.
Find the largest number whose square is less than or equal to the leading digit pair. In this case, the leading digit pair is 4; the largest number whose square is less than or equal to 4 is 2.
Put that number on the left side, and above the first digit pair.
2
--- ---- ----
2 | 4 66 56
Now square that number, and subtract from the leading digit pair.
2
--- ---- ----
2 | 4 66 56 |
-4
----
0
Extend the left bracket; multiply the last (and only) digit of the left-hand number by 2, put it to the left of the difference you just calculated, and leave an empty decimal place next to it
2
--- ---- ----
2 | 4 66 56 |
| -4
--------------
4 | 0
Then bring down the next digit pair and put it to the right of the difference.
2 1
--- ---- ----
2 | 4 66 56 |
| -4
--------------
41 | 0 66
-4
--------------
25
Now, repeat as before: Take the number in the left column (here, 41) and double its last digit (giving you 42). Copy this below in the left column, and leave a blank space next to it. (Double the last digit with carry: for example, if you had not 41 but 49, which is 40+9, you should copy down 40+18 which is 58.) Also, bring down the next digit pair on the right.
2 1
--- ---- ----
2 | 4 66 56 |
| -4
--------------
41 | 0 66
| -4
--------------
42 | 25 56
Now, find the largest digit like x such that 42x * x ≤ 2556. Here, it turns out that 426 * 6 = 2556 exactly.
2 1 6
--- ---- ----
2 | 4 66 56 |
| -4
--------------
41 | 0 66
| -4
--------------
42 | 25 56
56
---------------------
0
When the difference is zero, you have an exact square root and you're done. Otherwise, you can keep finding more decimal places for as long as you want.
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