How do you extract square root? - Answers

There are long division methods, and guess and divide methods. I'll go over the guess and divide method. Let's assume X is the number we want the square root of. The guess and divide consists of: 1. Guessing the square root of X (the guess is now known as Y1). 2. Divide X by Y1, and then using the resulting number as the new Y2. 3. Average Y1 and Y2, giving you the new number Y1. 4. Repeat steps 2-3 until your guess Y1 is roughly equal to the average of Y1 and Y2 Here's an example sqrt 695; my first guess for the root is 25. 1. 695 / 25 = 27.8 2. 25 + 27.8 / 2 = 26.4 3. 695 / 26.4 = 26.3257 4. 26.4 + 26.3257 / 2 = 26.36285 5. 695 / 26.36285 = 26.3628553 These two numbers are about equal, so you now have a good estimate of the root of 695. 26.3628553 *26.3628553 = 695.0001 You can keep going through the process until you are satisfied with the accuracy.