Question

Using rational approximations, what statement is true?(1 point)Responses49−−√>7start root 49 end root greater than 748−−√<36−−√start root 48 end root less than start root 36 end root48−−√>36−−√start root 48 end root greater than start root 36 end root49−−√<7

Answer 1

To determine which statements are true using rational approximations, let's evaluate each expression:

1. **\( \sqrt{49} > 7 \)**: This is false, because \( \sqrt{49} = 7 \).

2. **\( \sqrt{48} < \sqrt{36} \)**: This is false because \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \). Therefore, \( \sqrt{48} > \sqrt{36} \).

3. **\( \sqrt{48} > \sqrt{36} \)**: This is true because \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6\).

4. **\( \sqrt{49} < 7 \)**: This is false, because \( \sqrt{49} = 7 \).

From these evaluations, we conclude that the only true statement is:

**\( \sqrt{48} > \sqrt{36} \)**.