How do you extract square root?

Answer 1

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.