Question

find the least perfect square with 4 digits by division method​

Answer 1

Answer:

Least number of four digits = 1000.

(32)2 is more than 1000 by 24.

So, the least number to be added to 1000 is 24.

1000 + 24 = 1024

Therefore, the smallest four digit number which is a perfect square is 1024.

Step-by-step explanation:

Answer 2

The smallest four digit number is 1000. But 1000 is not a perfect square, so we need to examine the successors to 1000 that is 1001, 1002, 1003 and so on.

Now, we know that the last digit of the number which is a perfect square must be 1,4,5,6,9 or 0 and none of 1001, 1004, 1005, 1006, 1009 are perfect squares so there are no perfect square numbers between 1000 to 1009.

Next, the ten-digit perfect square can never be odd; that is 1, 3, 5, 7, 9. So the numbers between 1010 to 1019 cannot be a perfect square.

And, also the numbers 1020, 1021, 1022, 1023, 1027, 10 do not qualify the above criteria, so the numbers between 1020 to 1029 which are left out are 1024, 1025, 1026, 1029.

Let us check 1024, whether it is a perfect square or not ( see the above attachment)

Hence, The smallest four digit number which is a perfect square is 1024.