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.