Estimate the nearest perfect squares above and below the number
Find which two whole numbers the square root must be between
Use prime factorization if the number is a perfect square
Pair identical factors and take one from each pair
For non-perfect squares, use the long division square root method
Start by grouping digits in pairs from right to left
Find the largest square less than or equal to the leftmost group
Subtract, bring down the next pair, and continue
Use repeated approximation by testing nearby numbers
Check squares of decimals like 1.1, 1.2, 1.3, and so on
Use the average of a guess and number divided by the guess
Repeat the averaging process to improve accuracy
Memorize common square roots of perfect squares
Use estimation and comparison to narrow the answer quickly