How to manually find a square root ?
1Answer
First, divide the number to be square-rooted into pairs of digits, starting at the decimal point. That is, no digit pair should straddle a decimal point. (For example, split 46656 into "4 66 56")
Then you can put some lines over each digit pair, and a bar to the left, somewhat as in long division.
+--- ---- ---- | 4 66 56
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.
2 1 6
+--- ---- ----
2 | 4 66 56
|-4
+----
41 | 0 66
|- 41
+--------
426 | 25 56
|- 25 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.
- answered 6 years ago
- Community wiki
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