How to compute square root of integer with only add, sub, div and mult

Question

Tamed0g · Accepted Answer

f(x)=sqrt(x);

1. Find the integer (n) whose square (x0) is closest to x, e.g: n=sqrt(x0);

2. Use taylor expansion: f(x) = f(x0) + f'(x0)(x-x0) = n + 1/2n*(x-n^2);

Verify:

x=59;
x0=64;
n=8;
f(59) = 8+1/16*(59-64) =7.6875

zooboo · Answer

let y(x) = sqrt(x)
then guess a value guessY

now calculate mean(guessY+x/guessY) which is new guessY

keep doing until the relative error < epsilon

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