kill(all)$

van=facebook.com/LearningCalculus$

f(x):=2^(1/x);

g(x):=x^x;

h(x):=f(x)-g(x)$ h(x);

[sqrt(2),f(sqrt(2))];

newton(t):=float(subst(t,x,x-h(x)/diff(h(x),x)));

newton(sqrt(2));

bfloat(sqrt(2));