Question & Answer

Find the smallest 5 digit perfect square number.

ANSWER Verified Verified
Hint: Start from the smallest 5 digit number and check till you get a 5 digit number which is a perfect square. Use prime to find the square roots of each number.

Complete step by step answer:
Before proceeding with the solution, let’s understand the concept of prime factorization. A prime number is a number which is not divisible by any other number except 1 and itself. Any number can be expressed as a product of prime numbers. All the prime numbers, which when multiplied, give a product equal to a number (say x) are called the prime factors of the number x. To write the prime factors of a number, we should always start with the smallest prime number, i.e. 2 and check divisibility. If the number is divisible by the prime number, then we write the number as a product of the prime number and another number, which will be the quotient when the given number is divided by the prime number. Then, we take the quotient and repeat the same process. This process is repeated till we are left with 1 as the quotient.
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.
Therefore, the answer to the above question is 10000.

Note: While calculating square roots and cube roots, prime factorization is the easiest method. But it takes time. Hence, other methods should also be learnt, so that they can be used while solving problems in cases where time plays an important role.