Question

Using rational approximations, what statement is true?(1 point)%0D%0AResponses%0D%0A%0D%0A48−−√<36−−√%0D%0Astart root 48 end root less than start root 36 end root%0D%0A%0D%0A48−−√>36−−√%0D%0Astart root 48 end root greater than start root 36 end root%0D%0A%0D%0A49−−√>7%0D%0Astart root 49 end root greater than 7%0D%0A%0D%0A49−−√<7

Answer 1

To determine the truth of each statement using rational approximations, let's evaluate them one by one.

1. **\(\sqrt{48} < \sqrt{36}\)**

- We know that \(\sqrt{36} = 6\).
- For \(\sqrt{48}\), we can approximate it: \( \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \), which is approximately \( 4 \times 1.732 \approx 6.928 \).
- Therefore, \( \sqrt{48} \approx 6.928 \) and \( \sqrt{36} = 6 \).
- This statement is **false** because \( 6.928 > 6 \).

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

- As calculated, \( \sqrt{48} \approx 6.928 \) and \( \sqrt{36} = 6 \).
- Therefore, this statement is **true** because \( 6.928 > 6 \).

3. **\(\sqrt{49} > 7\)**

- We know that \(\sqrt{49} = 7\).
- Therefore, this statement is **false** because \( 7 \) is not greater than \( 7 \).

4. **\(\sqrt{49} < 7\)**

- Again, since \(\sqrt{49} = 7\), this statement is also **false** because \( 7 \) is not less than \( 7 \).

**Conclusion**: The true statement from the options is \(\sqrt{48} > \sqrt{36}\).