Estimate the nearest perfect squares around the number
Identify which two perfect squares the number lies between
Use a rough mental approximation based on closeness to those squares
Apply prime factorization if the number is a perfect square
Break the number into factors and simplify square pairs
Use the long division method for manual square root calculation
Use the Babylonian method by guessing and averaging repeatedly
Check your result by squaring the estimate
Refine the estimate until it is close enough
Memorize common square roots of perfect squares and common fractions