Question

What are some algorithms used to find square root(or to approximate them)? Say √2,√7

Answer 1

Probably the best approach is to use Newton's Method.

For example, for √7, you could note that this number is a root of the function f(x)=x2−7. Newton's Method is an iterative scheme based on the equation xn+1=xn−f(xn)f'(xn)=xn−x2n−72xn(the derivation of this is based on finding the x-intercept of the tangent line to the graph of f at the point (xn,f(xn))). Based on the initial guess x0=3, we would get x1=3−9−76=3−13=83≈2.66667as our next approximation (if you square this number, you'll get 649≈7.11111).

If you use Newton's Method one more time here, you'll get x2=83−649−7163=83−19163=83

HOPE IT HELPS YOU