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

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

Square Root by Prime Factors

To find the square root of a perfect square using prime factorization, we rely on the principle that a perfect square can be broken down into prime factors, where each factor's exponent is even and the square root is obtained by taking half of each exponent.

Here's a step-by-step explanation:

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

Step 2: Divide the power of each prime factor 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: Calculate the square root of 144, a perfect square.

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

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

Step 3: Multiply the prime factors using their reduced 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.