Eight Standard >> Method of finding square root of a perfect square number | Part-1

Square Root by Prime Factors

The prime factorization method for finding the square root of a perfect square number is based on the property that every perfect square can be expressed as the product of its prime factors, each raised to half of their respective powers.

Here's a step-by-step explanation:

Step 1: Write down the prime factorization of the given perfect square number "N."

Step 2: Divide each exponent of the prime factors by 2.

Step 3: Combine the prime factors with their halved exponents to get the square root of the perfect square.

Let's illustrate this method with an example:

Example: Find the square root of the perfect square number 144.

Step 1: Prime factorization of the number 144: \(2^4 * 3^2\)

Step 2: Halve the exponents: \(2^2 * 3^1\)

Step 3: Combine the prime factors with halved exponents: \(2^2 * 3\) = \(4 * 3\) = 12

The square root of 144 is 12.

The prime factorization method works for any perfect square number and provides an efficient way to find its square root by breaking down the number into its prime factors and then taking the square root of each factor raised to half of its exponent. This method is especially useful for larger perfect square numbers where long division may be more time-consuming.