Question

Find the smallest four digit number which is a perfect square.

Answer 1

Hint: Here, we need to use the rules of finding a perfect square and check whether the remaining numbers have any square root or not.

Complete step by step answer:
 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,

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

Note: A squares of all integers are called as perfect square numbers.
The alternative method of finding smallest four digit number which is a perfect square is explained below:
We know that the smallest 4 digit number is 1000. But it is not a perfect square number.
So, the smallest four digit number which is a perfect square must be near to 1000.
Let us try some numbers which is a perfect square,
\[\begin{align}
  & {{30}^{2}}=900 \\
 & {{31}^{2}}=961 \\
 & {{32}^{2}}=1024 \\
\end{align}\]
Hence, The smallest four digit number which is a perfect square is 1024.