1. The problem is to estimate the value of $\sqrt{74}$ without a calculator and determine between which two numbers it lies. 2. We know that $8^2 = 64$ and $9^2 = 81$. Since $74$ is between $64$ and $81$, $\sqrt{74}$ lies between $8$ and $9$. 3. To narrow it down further, check squares closer to 74: - $8.5^2 = 72.25$ - $8.6^2 = 73.96$ - $8.7^2 = 75.69$ 4. Since $74$ is greater than $73.96$ and less than $75.69$, $\sqrt{74}$ is between $8.6$ and $8.7$. 5. Therefore, $\sqrt{74}$ is between $8.5$ and $9$. Final answer: The best statement is Choice B: The value of $\sqrt{74}$ is between $8.5$ and $9$.