Question

Find the least number which is to be added to 1579 so as to make it a perfect square.

Answer 1

we know that  40 * 40 = 1600.  So we need to add 1600 - 1579 = 21 to make it a perfect square.

We have the given number as  1579..   The two digits 79 form one unit.  Then the two digits 15 form one pair.  15 is between squares of 3 and 4.  
 
         39
       =======
  3   |  15  79
           9
         =====
  69     6  79
          6  21
===========

hence, the square root of 1579 is between 39 and 40..  So we take the square of 40  minus 1579.  We get the answer.