There is better way and it only takes two or three iterations to calculate to many places.

Example you wish to find the square root of 600

1st you make a guess. a good gues would be about 25 but I will make a bad guess to show you how quickly the iterations work.

Guess square root of 600 is 10

1) Divide 10 into 600 giving you 60

2) Add you guess to the result and divide by 2.

(10 + 60)/ 2 = 35

3) divide the result into 600

35 into 600 gives 17.

Repeat #2 & 3

2) (35+17)/2 = 26

3) 600/26 = 23

Repeat 2 and that is your answer.

2) (26+23)/2= 24.5

The actual answer is 24.495

In other words, you guess the answer divide your guess into the number and add your guess to the result and divide by two.

That is your new more accurate guess. Do that again once or twice for very high accuracy. With a good guess it only take one time.

10 was a horrible guess just to show you how quickly the result gave you a new good guess.

Now I will explain how to make a good first guess.

I will give you two numbers.

56312.134

Start at the decimal point and go left two number at at time

5-63-12 you guess the square root of 5 say 2.5 and add 0’s for each pair. that gives you a guess of 2.5 *100 or 250

if the number was 563 you would guess 25

If the number was 5-63-12-45 you would guess 2500.

Now suppose it is an even number of digits left of the decimal such as 70123456 giving

70-12-34-56. Then you guess the square root of 70 say 8 and add three 0’s or 8000

Let try it.

70123456/8000 = 8765

add (8000 + 8765)/2 = 8383

The actual square root is 8374 so one more iteration would give you the answer.

If you wish to do it the old fashion way see :

27 x 27 = 729