Estimate between the nearest perfect squares
Identify the two perfect squares the number falls between
Decide which square it is closer to
Use repeated subtraction for perfect squares
Use prime factorization for perfect-square numbers
Pair identical factors to simplify the root
Use the long division square root method
Divide the number into pairs of digits from right to left
Find the largest square less than or equal to the leftmost pair
Subtract and bring down the next pair
Double the current root and find the next digit
Repeat until the desired accuracy is reached
Use approximation with nearby decimals
Check your answer by squaring it
Use known square roots as benchmarks
Memorize common square roots for faster estimation