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Step 4:   Subtract the product (square) from the first period (57 – 49 = 8).
                    Step 5:   Bring down the second period (15) and place it to the right of the remainder. This number (815)
                              forms the new dividend.
                    Step 6:   (i)  Double the quotient (7 × 2 = 14) and write it in the divisor’s place followed by a blank space.
                              (ii)  Fill the blank space with the largest number (5) such that 145 × 5 is less than 815. 145 is the
                                  new divisor.
                    Step 7:   Subtract the product (145 × 5 = 725) from the dividend obtained in step 5. Bring down the third
                              period (36) to the right of the remainder. This again forms the new dividend, i.e., 9,036.
                    Step 8:   Repeat steps 6, 7 till all the periods are exhausted.
                    Step 9:   The final quotient (756) is the square root of 5,71,536.


                        The number of bars is equal to the number of digits in the square root of the given number.

                    Example 17:     Find the least number that must be subtracted from 4,568 to make it    67
                                    a perfect square. Also, find the square root of the resulting number.     6   45 68
                    Solution:       The remainder is 79. It means that if 79 is subtracted from the        36
                                    given number, the remainder will be zero, and, the given number
                                    will become a perfect square.                                     127      968
                                    Thus, the least number to be subtracted is 79.                           889
                                    \  Perfect square = 4,568 – 79 = 4,489                                     79
                                      4,489  = 67

                    Example 18:     Find the least number that must be added
                                    to 8,902 to make it a perfect square. Find
                                    the square root of the perfect square so       94                       95
                                    obtained.                                 9    89 02               9    89 02

                                                     2
                    Solution:       It is clear that (94)  < 8,902 < (95) 2        81                       81
                                                                       2
                                    \   8,902 = (925 – 802) less than (95)    184       802         185       802
                                       = 123 less than (95) 2
                                    Thus, the least number to be added is            736                      925
                                    123.
                                    \  Perfect square = 8,902 + 123 = 9,025

                                      9,025  = 95

                    Example 19:     Find the least number of six digits that is a perfect square.
                    Solution:       Least six digit number = 1,00,000
                                    To find the least six digit number which is a perfect square, we need to find the least number
                                    that must be added to 1,00,000 to make it a perfect square.

                                                 316                                   317
                                            3    10 00 00                          3   10 00 00

                                                   9                                     9
                                           61      100                            61     100
                                                     61                                    61
                                          626        3900                        627       3900
                                                     3756                                  4389


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