Estimate the nearest perfect squares around the number
Identify which two perfect squares the number lies between
Use a rough approximation based on closeness to those squares
Apply the long division square root method
Pair digits from right to left before starting
Find the largest square less than or equal to the leftmost pair
Subtract and bring down the next pair
Double the current root and use it as the divisor guide
Choose the next digit so the product stays within the remainder
Repeat until the desired accuracy is reached
Use the average method by comparing with nearby squares
Refine the estimate by checking the square of your guess
Adjust the guess upward if the square is too small
Adjust the guess downward if the square is too large
Memorize common square roots of perfect squares for faster estimation