Question
Using rational approximations, what statement is true?(1 point)
Responses
49−−√<7
48−−√<36−−√
49−−√>7
48−−√>36−−√
Responses
49−−√<7
48−−√<36−−√
49−−√>7
48−−√>36−−√
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To evaluate which statement is true using rational approximations, let's approximate the values:
1. **For \( \sqrt{49} < 7 \)**:
- We know \( \sqrt{49} = 7 \). Thus, this statement is **false**.
2. **For \( \sqrt{48} < \sqrt{36} \)**:
- \( \sqrt{48} \) is approximately \( 6.93 \) and \( \sqrt{36} = 6 \).
- So \( \sqrt{48} > \sqrt{36} \), making this statement also **false**.
3. **For \( \sqrt{49} > 7 \)**:
- We already established that \( \sqrt{49} = 7 \). Thus, this statement is **false**.
4. **For \( \sqrt{48} > \sqrt{36} \)**:
- As calculated earlier, \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \), thus \( \sqrt{48} > \sqrt{36} \) is **true**.
In conclusion, the true statement is:
**\( \sqrt{48} > \sqrt{36} \)**.
1. **For \( \sqrt{49} < 7 \)**:
- We know \( \sqrt{49} = 7 \). Thus, this statement is **false**.
2. **For \( \sqrt{48} < \sqrt{36} \)**:
- \( \sqrt{48} \) is approximately \( 6.93 \) and \( \sqrt{36} = 6 \).
- So \( \sqrt{48} > \sqrt{36} \), making this statement also **false**.
3. **For \( \sqrt{49} > 7 \)**:
- We already established that \( \sqrt{49} = 7 \). Thus, this statement is **false**.
4. **For \( \sqrt{48} > \sqrt{36} \)**:
- As calculated earlier, \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \), thus \( \sqrt{48} > \sqrt{36} \) is **true**.
In conclusion, the true statement is:
**\( \sqrt{48} > \sqrt{36} \)**.
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