Question

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

Answer 1

To determine which statement is true using rational approximations, let's analyze each one:

1. **\( \sqrt{49} > 7 \)**: This statement is false because \( \sqrt{49} = 7 \).
2. **\( \sqrt{49} < 7 \)**: This statement is also false because \( \sqrt{49} = 7 \).
3. **\( \sqrt{48} > \sqrt{36} \)**: Let's approximate:
- \( \sqrt{48} \) is slightly less than \( \sqrt{49} \), which is 7, so \( \sqrt{48} \) is approximately 6.928.
- \( \sqrt{36} = 6 \).
- Since \( 6.928 > 6 \), this statement is true.
4. **\( \sqrt{48} < \sqrt{36} \)**: This statement is false because we just established that \( \sqrt{48} > \sqrt{36} \).

Thus, the true statement is:

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