Question

Using rational approximations, what statement is true?(1 point)
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:

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

Related Questions