kill(all)$

van=facebook.com/LearningCalculus$

f(x,y):=(y+x)/(sqrt(y)+sqrt(y+x)) + (y-x)/(sqrt(y)-sqrt(y-x)) - sqrt(y);

newton(t,y):=float(subst(t,x,x-f(x,y)/diff(f(x,y),x)))$
figNewton(t,y):=newton(newton(newton(newton(newton(sqrt(y+1),y),y),y),y),y);

f(sqrt(3),2);

figNewton(sqrt(3),2);

float(sqrt(3));

float(f(figNewton(sqrt(3),2),2));

for a: 2 thru 10 do
print ("Answer: ", figNewton(a,a));