# How to check if a number is a perfect square?

A number is a perfect square if given number is equal to the square of some natural number.

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

## Examples on How to check if a number is a perfect square

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.

Example 2: Is 784 a perfect square?
Step 1: Finding prime factors of 784 Step 2: Grouping factors in pairs as shown below784=(2×2)x(2×2)x(7×7)
Step3: After grouping we notice that no factor is left
Therefore, we can conclude that 784 is absolutely a perfect square.

Example 3: Is 3721 a perfect square?
Step 1: Finding prime factors of 3721. Step 2: Grouping factors in pairs as shown below
3721=(61×61)
Step 3: After grouping we notice that no factor is left
Therefore, we can conclude that 3721 is absolutely a perfect square.

Example 4:Is 6889 a perfect square?
Step 1: Finding prime factors of 6889. Step2: Grouping factors in pairs as shown below
6889=(83 x 83)
Step 3:After grouping we notice that no factor is left
Therefore, we can conclude that 6889 is absolutely a perfect square.
Tip: Remember the squares of prime numbers as it can save a lot of time.