Question

Find the least number of 4 digits which is a perfect square.

Answer 1

The least number with four digits is 1000. To find the least square number with four digits, we must find the smallest number that must be added to 1000 in order to make a perfect square. For that, we have to find the square root of 1000 by the long division method as shown below:

1000 is 24 (124 − 100) less than the nearest square number 32². Thus, 24 must be added to 1000 to be a perfect square.
1000 + 24 = 1024
Hence, the smallest perfect square number with four digits is 1024.