How to manually find a square root ?

546

Find the square root of 46656 number

  • Math

  • asked 1 month ago
  • B Butts

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0

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 1 month ago
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