Question

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

Answer 1

To evaluate the statements using rational approximations, let's first calculate the square roots of the numbers involved.

1. **Calculating √49**:
\[
\sqrt{49} = 7
\]

2. **Calculating √48**:
Since 48 is between 36 (6²) and 49 (7²), we can approximate:
\[
\sqrt{48} \approx 6.93 \quad (\text{since } 48 \text{ is close to } 49)
\]

3. **Calculating √36**:
\[
\sqrt{36} = 6
\]

Now we evaluate each statement:

1. \( \sqrt{49} > 7 \):
- False, because \( \sqrt{49} = 7 \).

2. \( \sqrt{48} < \sqrt{36} \):
- False, because \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \).

3. \( \sqrt{48} > \sqrt{36} \):
- True, because \( \sqrt{48} \approx 6.93 \) is greater than \( 6 \).

4. \( \sqrt{49} < 7 \):
- False, because \( \sqrt{49} = 7 \).

Thus, the true statement is:
\[
\sqrt{48} > \sqrt{36}
\]