World's Fastest Square Root: Newton's Method

Newton's method, from 1670, is a crazy fast way of generating square roots. The number of accurate digits in the square root doubles every single step.

It is derived by taking the Newton Raphson equation
https://en.wikipedia.org/wiki/Newton%...

and plugging in the equation for a square as the function x^2 = a

Images I used

newton https://pixabay.com/vectors/isaac-new...
telescope https://en.wikipedia.org/wiki/File:Ne...
prism https://en.wikipedia.org/wiki/File:Di...
Mercury https://commons.wikimedia.org/wiki/Fi...
calculus https://commons.wikimedia.org/wiki/Fi...
Newton Apple https://commons.wikimedia.org/wiki/Fi...
laws of motion https://commons.wikimedia.org/wiki/Fi...
quarter https://pixabay.com/photos/coin-quart...
chemistry https://pixabay.com/photos/test-tube-...
binomial https://pixabay.com/vectors/bayesian-...