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# How to Find Square Roots of a Number by Prime Factorization?

August 28, 2022 written by Azhar Ejaz

To calculate the square root of any number, we need to figure out whether the given number is an imperfect square or a perfect square. If the number is an imperfect square, such as 2, 3, 5, etc., then we have to use a long division method to determine the root. If the number is a perfect square, such as 4, 9, 16, etc., then we can factorize the number by the prime factorization method.

There are four methods to calculate the square roots of the numbers are

• Square Root by Prime Factorization
• Square Root by Long Division Method
• Square Root by Repeated Subtraction Method
• Square Root by Estimation Method

In this article How to find the square roots of the numbers by using prime factorization.

## Square Roots by Prime factorization

Prime factorization of any number means denoting that number as a product of prime numbers. To determine the square root of a given number by using the prime factorization method, we follow the steps given below:

Step 1: Divide the given number into its prime factors.

Step 2: Form pairs of similar factors such that both factors in each pair are equal.

Step3: Take one factor from the pair.

Step 4:  Determine the product of the factors obtained by taking one factor from each pair.

Step 5: That product is the square root of the given number.

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