Concept :1 Mark
Application :1 Mark
Calculation : 1 Mark
We know that the least number of 4 digits is 1000.
In order to find the least number of four digits which is a perfect square, we must first find the smallest number that must be added to 1000 to make it a perfect square. For this, we work out the process of finding the square root by long division method as given below.
313¯¯¯¯¯¯10 ¯¯¯¯¯¯00961 100 61 39
323¯¯¯¯¯¯10 ¯¯¯¯¯¯00962 100 124
It follows from this that 1000 is (124 - 100) = 24 less than (32)2. Thus, if we add 24 to 1000, it becomes a perfect square.
Hence, the smallest number of four digits which is a perfect square is (1000 + 24) = 1024.