Find the least perfect square with four digits.

We need to find out the least perfect square with four digits

Let us consider a four digit number as 1000 which is not a perfect square.

Now, we must find out a number when it is added to this number the resultant number will be a perfect square.

Using division method we get

We know that 1000 lies between 31² and 32²

⇒ 31² < 1000 < 32²

⇒ 32² – 1000

= 1024 – 1000

= 24

24 must be added to 1000 we get 1024

Hence, the least perfect square with four digit is 1024