1. The problem asks to find the position of $\sqrt{89}$ on the number line. 2. We know that $\sqrt{89}$ is the positive number which when squared gives 89. 3. To estimate $\sqrt{89}$, find perfect squares near 89: $9^2 = 81$ and $10^2 = 100$. 4. Since $81 < 89 < 100$, $\sqrt{89}$ lies between 9 and 10. 5. To get a better estimate, calculate $\sqrt{89} \approx 9.433$ (since $9.433^2 \approx 89$). 6. On the number line, points are labeled as: - A at 8 - B at 8.5 - C at 9 - D at 10 7. Since $9 < 9.433 < 10$, $\sqrt{89}$ lies between points C and D. 8. Therefore, the point closest to $\sqrt{89}$ is between C (9) and D (10), closer to D. Final answer: $\sqrt{89}$ is between points C and D, approximately at 9.433.