Finding Square Roots by Prime Factorization

Finding the square root using prime factorization is a method where a composite number is broken down into its prime factors. By grouping these prime factors into pairs of identical numbers, one factor from each pair is taken to find the square root. This method is most efficient for small or medium-sized numbers that can be easily factored.

sqrt(a * a * b * b) = a * b

Worked examples

• • Forgetting to group the prime factors into pairs before extracting them.
• • Using composite numbers instead of prime numbers during the factorization steps.