QUESTION

Find the smallest 5 digit perfect square number.

For example: Consider the number 51. It is an even number. So, it is not divisible by 2. The sum of the digits of 51 is 5 + 1 = 6. Hence, 51 is divisible by 3. Now, $51=3\times 17$ . Now, we take 17. We know, 17 is a prime number. Hence, the prime factors of 51 are 3 and 17.
Now, coming to the question, we need to start checking from the smallest two digit number, if it is a perfect square or not till we find a five digit number, which is a perfect square. So, the smallest 5 digit number is 10000, and we know that 10000 is a perfect square and can be written as $10000=100\times 100$ . So, 10000 is the smallest 5 digit number to be a perfect square.