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MATHEMATICS FOR AIR CREW TRAINEES     18

 a. Begin at the decimal point and point off as many periods of two digits each as possible. Point off to the left if the number is an integer, to the right if it is a decimal. Point off to both the left and the right if there are digits both left and right of the decimal point. If the last period of the decimal has but one digit, add a cipher to complete the period.

 b. Find the largest integer the square of which is equal to or less than the left-hand group, and write this integer for the first digit of the root and directly over the first group of digits.

 c. Square the first digit of the root; subtract its square from the first group and bring down the second group.

 d. Obtain a trial divisor by doubling the partial root already found, divide it into the remainder (omitting from the latter the right-hand digit), and write the integral part of the quotient as the next digit of the root and directly over the group of digits used in determining it.

 e. Annex the root digit just found to the trial divisor to make the complete divisor; multiply the complete divisor by this root digit; subtract the result from the dividend; bring down the next group for a new dividend. 

 f. Obtain a new trial divisor by doubling the part of the root already found, and proceed as before until the desired number of digits of the root have been found. 

 g. After extracting the square root of a number involving decimals, point off one decimal place in the root for every decimal group in the number.

 h. If the root is exact, square it. The result should be the original number. If the root is inexact, square it and add to this result the remainder.

Example: Find √681.9213
Solution:
  26.  1 1
√681. 92 13

 46 
  6
----
276
  521
    1
  ---
    5221
       1
    ----
    5221

4
---
2 81

2 76
-------
   5 92

   5 21
  --------
     71 13

     52 21
    -------
        1892

 (1) Point off in groups of two in both directions from the decimal point.
 (2) 2 is the largest integer the square of which is equal to or less than 6, so place the 2 over the 6. 
 (3) Square 2 and place it under the 6. Subtract.
 (4) Bring down 81, the next two digits.
 (5) Bring down the 2 above the 6 and double it for the trial divisor. Divide the 4 into 28, the remainder less the last digit to the right; 7 is obtained.

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