Question

Find the square root to the fourth decimal place by the division method of 5328

Answer 1

Group the digits in the given  number - 2 digits by two digits from units side towards the most significant digit (highest digit).  Now find X so that X * X <= 53. So X = 7. This is highest but X^2 < 53.  Write 7 above 53 and on the left side.
Now multiply 7 * 7 and write it below 53. subtract.
Now, import 28 to right side of 4. 
Write two times 7 (from above top of 53) to the left of 428.  Find a digit N such that (140+N) * N  <= 428. Here i find 2 that is, 142*2 = 284. but 143*3=429 which is more than 428. Now subtract 284 from 428. Write a decimal place on the number on top. Repeat the procedure by importing 00. Write twice 72 to left of 14400. find X such that (144*10+X ) X <= 14400

           7 2 . 9 9 3 0    <<<==== this is teh square root
       ===============================================
           |    53     28
7         |    49
           |  ===
142     |      4 2 8
          |      2 8 4
           |  =======
           |      1 4 4 0 0
1449    |      1 3 0 4 1
           |===============
           |        1 3 5 9 0 0
 14589  |        13 1 3 0 1
           |==============
            |              4 5 9 9 0 0
145983  |             4 3 7 9 4 9
           =================
                             2 1 9 5 1 00
1459860