if you want to know where the expression for sqrt(a+b) come from it is a taylor series expansion of the first order (linear approximation) of f(x)=sqrt(a+x) aro

if you want to know where the expression for sqrt(a+b) come from it is a taylor series expansion of the first order (linear approximation) of f(x)=sqrt(a+x) arount 0. f'(x)= 1/(2*sqrt(a+x)). For x close to 0 you get f(x)≈f(0)+x*f'(0)