I would be grateful if someone could explain the following method of calculating a square root. I've numbered all the steps for reference.
I found various approximate methods in google. These methods were quite clearly iterating to the nearest value below the exact value, depending on the number of digits specified. But, in iterating, it seemed that ANY of the digits could change from one iteration to a slightly better iteration.
On the other hand, the guy below finds the FIRST digit after the point, then keeps that digit constant and finds the SECOND digit, then the THIRD and so on.
Thanks.
Alright, this is how I calculated the square root of 4692.
(1) First I tried to calculate to the closest large square number that is below 4692.
(2) 68x68 = 4624.
(3) 4692 - 4624 = 68.
(4) the next step is to calculate the first decimal place.
(5) 68 / 10 = 6,8.
(6) The first decimal can’t be 5 or higher because:
(7) 6,85 x 5= 34,25
(8) 34,25 x 2 = 68,50.
(9) 68,50 is bigger than 68 so the first decimal is smaller than 5.
(10) 6,84 x 4 = 27,36.
(11) 27,36 x 2 = 54,72.
(12) The first decimal is thus 4. Up to the next decimal.
(13) 68 - 54,72 = 13,28.
(14) 13 is close to 6,84 times 2 but just below it so the first number we can try is 9.
(15) 0,6849 x 9 = 6,1641.
(16) 6,1641 x 2 = 12,3282.
(17) because 9 is the highest number possible as a decimal and 12,3282 is the closest to 13,28, we now know that the second decimal is 9. Now the third decimal.
(18) I couldn’t do the same here as with the other two decimals. The third decimal I got by just checking and multiplying.
(19) I checked 68,499^2:
(20) 68,499 x 68,499 = 4692,113001.
(21) 68,499 x 68,499 is too big so I guessed that the third decimal would be 8 and it was.
(22) The square root of 4692 was ~68,498.