Find the smallest and the greatest 4-digit numbers, each of which is a perfect square.

The smallest 4-digit number = 1000

As we can see 1000 is not a perfect square.

Clearly, 1000 is greater than 31².

∴ On adding the required number to 1000, we shall be getting 32² i.e, 1024

So, the required number = 1024 -1000 = 24.

1000 + 24 = 1024 is a perfect square.

The greatest 4-digit number = 9999

Clearly, 9999 is greater than 99².

∴ On subtracting the required number to 9999, we shall be getting 99² i.e, 9801.

So, the required number = 9999 - 198 = 9801.

Hence, 1024 and 9801 are the smallest and greatest 4-digit number.