In 1224, Leonardo of Pisa, better known as Fibonacci, answered a mathematical challenge of John of Palermo in the presence of Emperor Frederick II: find a root of the equation x3 +2x2 +10x = 20. He first showed that the equation had no rational roots and no Euclidean irrational root-that is, no root in any of the forms a±√b,√ a±√b, √(a ±√b), or √√((a) ±√b), where a and b are rational numbers. He then approximated the only real root, probably using an algebraic technique of Omar Khayyam involving the intersection of a circle and a parabola. His answer was given in the base-60 number system as
1 + 22(1/60)+ 7(1/60)2 + 42(1/60)3 + 33(1/60)4+ 4(1/60)5+ 40(1/60)6.
How accurate was his approximation?