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: \[ \sqrt{48} > \sqrt{36} \]