Chapter 1 - Foundations for Algebra - 1-3 Real Numbers and the Number Line - Practice and Problem-Solving Exercises - Page 21: 65

Fibonacci's estimate is more accurate because it's value is closer to $\pi$

$\pi \approx$ 3.142 $\sqrt 10$ = 3.162 $\frac{864}{275}$ = 3.1418 $\approx$ 3.142 Therefore, $\frac{864}{275}$ is closer to the value of $\pi$, and thus Fibonacci's estimate is more accurate.