I've always been curious how this is done. I've had a lot of math but never seen anything that shows how to do it.
2006-09-08 08:49:56 · 9 answers · asked by duck_marsh 1 in Science & Mathematics ➔ Mathematics
I don't mean simply pressing the button...I mean that actual mathematics behind the algorithm...
2006-09-08 08:51:20 · update #1
Computer and calculator use numerical algorithms for that.
Most of them is obtained by the Taylor´ seriess
f(x) = f(a) + (x-a)f´(a)/1! + (x-a)^2.f´´(x)/2! ... because the right side is a polynomial function and is ease to create a computer program.
The first terms of Taylor´serie for the function y = sqrt(x) are:
sqrt(x) = 1 + (x-1)/2 - (x-1)^2/8 + (x-1)^3/16 - 5(x-1)^4/28 ...
There are problems of approximations... to get high precision it is necessary to use several terms of the series.
2006-09-08 10:13:16 · answer #1 · answered by vahucel 6 · 0⤊ 0⤋
Take a raffle on the sq. root--some thing life like will do. you could %. some thing unreasonable, too, in basic terms no longer 0: it in basic terms takes longer. call your guess A. Your decision, I shall call N. Compute: B=N/A Compute: C=(A+B)/2 Now, enable us assume A>B for the needs of argument. If that's no longer, in basic terms change 'em so that's real... in any case, Compute C' = N/C If C > C' then A = C If C = C' then you really've were given your sq. root, properly there! If C < C' then B = C Now, recompute C = (A+B)/2 bypass again and recompute C' and attempt this all yet over again. ultimately, you'll attain a level the position C-C' is smaller than your calculator can manage; you're actually there. word that the area between A & B distinctly a lot drops by technique of 0.5 each and each and every time you run by this cycle... it is amazingly quick: in 10 repetitions, you're interior a million section in a unmarried thousand; in 20, a million in a million; in 30, a million in one thousand million...
2016-11-06 22:12:51 · answer #2 · answered by ? 4 · 0⤊ 0⤋
There are several ways to do it, and I wouldn't know for sure what is usually done in a calculator, but one way is a simple formula which I can never remember. You can start with any guess, run it through the formula a few times, and arrive at the square root.
It could use a table of values, and interpolate and/or use trial and error between the table values.
I'm sure there are others, but I'm no mathemetician.
2006-09-08 09:51:31 · answer #3 · answered by Ken H 4 · 1⤊ 1⤋
The following page explains indepth different formulas for figuring square root, as well as codes used by computer programmers, to program calculators
2006-09-08 09:00:26 · answer #4 · answered by MattinCR 2 · 1⤊ 0⤋
i think there might be a table of numbers for example it'll have
2squared = 4
3squared =9
lets say you give it square root of 2.5
it'll find the mean of 4 and 9
2006-09-08 08:53:42 · answer #5 · answered by sur2124 4 · 1⤊ 2⤋
Trial and error. It guesses and checks until it gets within a certain accuracy tolerance.
2006-09-08 09:05:19 · answer #6 · answered by Anonymous · 1⤊ 1⤋
Who knows. I just use the button because it is harder without the calculator.
2006-09-08 08:52:47 · answer #7 · answered by dancer 2 · 0⤊ 2⤋
The CORDIC method.
2006-09-08 09:54:25 · answer #8 · answered by Andy S 6 · 0⤊ 0⤋
very quickly!
2006-09-08 08:51:25 · answer #9 · answered by Big hands Big feet 7 · 0⤊ 2⤋