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

Question

Responses

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

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−−√

Answer 1

To determine which statement is true using rational approximations, let's evaluate each option:

1. \( \sqrt{49} < 7 \):

   • \( \sqrt{49} = 7 \)
   • So, this statement is false.

2. \( \sqrt{49} > 7 \):

   • As established, \( \sqrt{49} = 7 \)
   • So, this statement is false.

3. \( \sqrt{48} < \sqrt{36} \):

   • \( \sqrt{48} \approx 6.93 \) (since \( 7^2 = 49 \) and \( 6.93^2 \) is very close to 48)
   • \( \sqrt{36} = 6 \)
   • Since \( 6.93 > 6 \), this statement is false.

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

   • As calculated, \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \)
   • Since \( 6.93 > 6 \), this statement is true.

Therefore, the true statement is: \( \sqrt{48} > \sqrt{36} \).