Question

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 greater than start root 36 end root

49−−√<7
start root 49 end root less than 7

48−−√<36−−√

Answer 1

To evaluate the statements using rational approximations, let's compute the values of the square roots:

1. **√49 > 7:**
\[
\sqrt{49} = 7 \quad \text{(False)}
\]

2. **√48 > √36:**
\[
\sqrt{48} \approx 6.93 \quad \text{and} \quad \sqrt{36} = 6 \quad \text{(True)}
\]

3. **√49 < 7:**
\[
\sqrt{49} = 7 \quad \text{(False)}
\]

4. **√48 < √36:**
\[
\sqrt{48} \approx 6.93 \quad \text{and} \quad \sqrt{36} = 6 \quad \text{(False)}
\]

The only true statement based on these evaluations is:

**√48 > √36**.