Group the digits of the number into pairs from right to left
Write the largest whole number whose square is less than or equal to the leftmost pair
Write that number as the first digit of the square root
Subtract its square from the leftmost pair
Bring down the next pair of digits to the right of the remainder
Double the current root and write it as the trial divisor prefix
Find the largest digit x such that the new divisor formed by adding x to the prefix and multiplying by x does not exceed the current dividend
Write x as the next digit of the square root
Multiply the full trial divisor by x and subtract the result
Bring down the next pair and repeat the same steps
Continue until all pairs are used or the required decimal places are obtained
Place the decimal point in the square root directly above the decimal point in the original number
If needed, continue the process by bringing down pairs of zeros after the decimal point