function sa=my_sqrt2(a)

eps=5*10^(-5); % tolerance
Nmax=10; % maximum number of iterations
x0=2; % initial guess

for i=1:Nmax
    x1=(x0+a/x0)/2
    if abs(x1-x0)<eps
        sa=x1;
        break
    else
        x0=x1;
    end
    if i==Nmax
        disp('Maximum number of iterations exceeded')
    end
end


function sa=my_sqrt3(a)

eps=5*10^(-5); % tolerance
Nmax=10; % maximum number of iterations
x0=a; % initial guess

for i=1:Nmax
    x1=(x0^3+3*x0*a)/(3*x0^2+a)
    if abs(x1-x0)<eps
        sa=x1;
        break
    else
        x0=x1;
    end
    if i==Nmax
        disp('Maximum number of iterations exceeded')
    end
end

format long
my_sqrt3(2)

x1 =

   1.428571428571429


x1 =

   1.414213926776741


x1 =

   1.414213562373095


ans =

   1.414213562373095

my_sqrt2(2)

x1 =

   1.500000000000000


x1 =

   1.416666666666667


x1 =

   1.414215686274510


x1 =

   1.414213562374690


ans =

   1.414213562374690

diary off