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

Question

Responses

48−−√<36−−√
start root 48 end root less than start root 36 end root

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

48−−√>36−−√
start root 48 end root greater than start root 36 end root

49−−√>7

Answer 1

To analyze the statements using rational approximations, we can evaluate the square roots:

1. \( \sqrt{48} < \sqrt{36} \): This is false because \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \).

2. \( \sqrt{49} < 7 \): This is false because \( \sqrt{49} = 7 \).

3. \( \sqrt{48} > \sqrt{36} \): This is true because as noted earlier, \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \), so \( 6.93 > 6 \).

4. \( \sqrt{49} > 7 \): This is false because \( \sqrt{49} = 7 \).

Therefore, the true statement is:

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