To find the square root of a number, there are several methods depending on whether the number is a perfect square or not:
- Repeated Subtraction Method (for perfect squares): Subtract consecutive odd numbers from the original number until you reach zero. The count of subtractions is the square root.
- Prime Factorization Method (for perfect squares): Express the number as a product of prime factors, group the factors into pairs, take one factor from each pair, and multiply them to get the square root.
- Estimation Method: Find the nearest perfect squares around the number and estimate the square root by approximation, refining the estimate step by step.
- Long Division Method (for any number): A digit-by-digit method similar to long division to find the exact square root including decimal places.
The most general method to find the square root, even for non-perfect squares, is the long division method. The other methods are simpler but mostly for perfect squares or approximations.
