1. The problem asks for the best approximation of $\sqrt{91}$.\n\n2. We note the perfect squares near 91: $81 = 9^2$ and $100 = 10^2$.\n\n3. Since $91$ is between $81$ and $100$, its square root is between $9$ and $10$.\n\n4. To narrow it down, compute or estimate: $9^2 = 81$, $9.5^2 = 90.25$, $9.6^2 = 92.16$.\n\n5. Since $91$ is closer to $90.25$ than $92.16$, $\sqrt{91} \approx 9.5$ to $9.55$.\n\n6. Therefore, the best approximation place $\sqrt{91}$ between $9$ and $10$.