1. **Problem:** Identify the correct values of labeled points P, Q, R, and S on the number line given their square roots. 2. **Step:** Calculate approximate values of each square root: - $\sqrt{64} = 8$ - $\sqrt{86} \approx 9.27$ - $\sqrt{102} \approx 10.1$ - $\sqrt{50} \approx 7.07$ - $\sqrt{62} \approx 7.87$ - $\sqrt{91} \approx 9.54$ - $\sqrt{101} \approx 10.05$ - $\sqrt{48} \approx 6.93$ 3. **Step:** Match these values to the number line points: - P is near 8, so $\sqrt{64} = 8$ fits best. - R is near 9.3, so $\sqrt{86} \approx 9.27$ fits best. - Q is near 10.1, so $\sqrt{102} \approx 10.1$ fits best. - S is near 7.07, so $\sqrt{50} \approx 7.07$ fits best. 4. **Conclusion:** Option A matches these values correctly. --- 1. **Problem:** Find the approximate height of a square fence section with area 75 sq ft. 2. **Formula:** Area of square $A = s^2$ where $s$ is side length. 3. **Step:** Solve for $s$: $$s = \sqrt{75}$$ 4. **Step:** Calculate: $$s \approx 8.66$$ 5. **Conclusion:** Closest option is H, 8.6 ft. --- 1. **Problem:** Find between which two whole numbers $\sqrt{88.6}$ lies. 2. **Step:** Calculate approximate value: $$\sqrt{88.6} \approx 9.41$$ 3. **Conclusion:** Lies between 9 and 10, so answer is C. --- 1. **Problem:** Identify which point best represents $\sqrt{57}$ on the number line. 2. **Step:** Calculate approximate value: $$\sqrt{57} \approx 7.55$$ 3. **Step:** Points are 6 (M), 7 (N), 8 (R), 9 (S). 4. **Conclusion:** Closest is point R (8), so answer is H. --- 1. **Problem:** Find between which two whole numbers length $PQ = \sqrt{116}$ lies. 2. **Step:** Calculate approximate value: $$\sqrt{116} \approx 10.77$$ 3. **Conclusion:** Lies between 10 and 11, so answer is B.