How to check if a number is a perfect square?

Using the prime factorization method we can find out if a given number is a perfect square or not. Moreover, by this method you can accurately say whether a number is a perfect square or not. We will not guess the answer as we all know that there is penalty for every wrong answer.

Prime numbers between 1 to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

Let us now go through the steps

Step 1: Find prime factors of the given number

Step 2 : Group the factors in pairs

Step 3: After grouping if you find that

          → The number is a perfect square if No factor is left

          → Number is not perfect square if Factor/Factors are left

We shall now apply this trick in our example

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Example 1:Is 1024 a perfect square?

Step 1: Finding prime factors of 1024

Step 2: Grouping factors in pairs as shown below 1024=(2×2)x(2×2)x(2×2)x(2×2)x(2×2)

Step 3:After grouping we notice that no factor is left
Therefore, we can conclude that without doubt 1024 is a perfect square.

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Step3: After grouping we notice that no factor is left
Therefore, we can conclude that 784 is absolutely a perfect square.

Also Read  How to verify if a number is a perfect cube?