How do calculators calculate roots?

Question

Mathematics

selection method or takes existing values?

Answer 1

Googled for you: https://thequestion.ru/questions/147403/kak-kalkul...

The most realistic thing in the conditions of the extremely limited amount of computing power of the calculator is the use of Newton's method. For the square root, it is, briefly and simply, as follows.
Let, for example, search for the root of the number 13. We take any number as an answer. For example, unit. We consider half the sum of the values ​​\u200b\u200bof this possible answer and the original number divided by this “answer”:
(1 + 13/1) / 2 = 7
Now the likely answer will be 7. Repeat the technique a few more times:
(7 + 13/7) / 2 = 4.4286
(4.4286 + 13/4.4286) / 2 = 3.682 (3.682 + 13/3.682) /
2 = 3.606
Etc. Already, the error is very small: if you check and square 3.606, you get 13.0057. It is very easy for a calculator to do additions and a little more difficult to divide, but it can carry out a chain of such operations quite quickly.

Answer 2

I heard that many functions are calculated through Chebyshev polynomials (approximation).

Answer 3

Most likely, they are laid out in a Taylor series
. In general, the "selection method" (it is called the "Method of half division") solve equations (the EMNIP mathematical apparatus does not allow (in general terms) to solve equations of degree higher than 5 in the "normal" way).
In general, your question is a matan from the first year of the institute.