1.6 is the 5-th root of 10 rounded off. But the 5-th power of the golden ratio is very close to 11, not 10, because 11 is the 5-th Lucas number and L_n = φ^n +

1.6 is the 5-th root of 10 rounded off. But the 5-th power of the golden ratio is very close to 11, not 10, because 11 is the 5-th Lucas number and L_n = φ^n + (-1/φ)^n.