Question

complete the number sentence with a <, >, or = sign. then choose the correct answer. a. $\sqrt{32} \square 5.1$ b. $\sqrt{17} \square \frac{9}{2}$ c. $\sqrt{49} \square 7.5$ d. $\sqrt{99} \square \frac{26}{3}$

Explanation:

To solve this problem, we need to compare the square root values with the given numbers and determine which inequality holds (either \( < \) or \( > \)). Let's analyze each option:

Option A: \( \sqrt{32} \square 5.1 \)

1. Calculate \( \sqrt{32} \):

• \( \sqrt{32} \approx 5.656 \) (since \( 5.656^2 \approx 32 \))

1. Compare with \( 5.1 \):

• \( 5.656 > 5.1 \), so \( \sqrt{32} > 5.1 \)

Option B: \( \sqrt{17} \square \frac{9}{2} \)

1. Calculate \( \sqrt{17} \) and \( \frac{9}{2} \):

• \( \sqrt{17} \approx 4.123 \)
• \( \frac{9}{2} = 4.5 \)

1. Compare:

• \( 4.123 < 4.5 \), so \( \sqrt{17} < \frac{9}{2} \)

Option C: \( \sqrt{49} \square 7.5 \)

1. Calculate \( \sqrt{49} \):

• \( \sqrt{49} = 7 \)

1. Compare with \( 7.5 \):

• \( 7 < 7.5 \), so \( \sqrt{49} < 7.5 \)

Option D: \( \sqrt{99} \square \frac{26}{3} \)

1. Calculate \( \sqrt{99} \) and \( \frac{26}{3} \):

• \( \sqrt{99} \approx 9.949 \)
• \( \frac{26}{3} \approx 8.666 \)

1. Compare:

• \( 9.949 > 8.666 \), so \( \sqrt{99} > \frac{26}{3} \)

If the problem is to find which one has \( < \), then:

• Option B: \( \sqrt{17} < \frac{9}{2} \)
• Option C: \( \sqrt{49} < 7.5 \)

If the problem is to find which one has \( > \), then:

• Option A: \( \sqrt{32} > 5.1 \)
• Option D: \( \sqrt{99} > \frac{26}{3} \)

Assuming the problem is to find the one with \( < \) (common in such problems), the answers are:

• For \( < \): B. \( \sqrt{17} < \frac{9}{2} \), C. \( \sqrt{49} < 7.5 \)
• For \( > \): A. \( \sqrt{32} > 5.1 \), D. \( \sqrt{99} > \frac{26}{3} \)

If we need to pick one (e.g., the most probable \( < \) case), then:

Answer:

B. \( \sqrt{17} < \frac{9}{2} \) (or C. \( \sqrt{49} < 7.5 \) depending on the exact question)