kill(all)$

fpprintprec:20$

van=facebook.com/LearningCalculus$

f(x):= ''(fullratsimp(sqrt(x*sqrt(2-x^2)+1)-2*sqrt(5)*(1-x^2)));

newton(t):=float(subst(t,x,x-f(x)/diff(f(x),x)))$

newton(0.82930699989815559);

float(f(sqrt(1-sqrt(39)/20)));