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

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

49−−√>7
start root 49 end root greater than 7

49−−√<7

Answer 1

To analyze the statements, let's evaluate each one.

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

   • \(\sqrt{48} \approx 6.93\)
   • \(\sqrt{36} = 6\)
   • Thus, \(\sqrt{48} > \sqrt{36}\) is true.

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

   • As noted above, \(\sqrt{48} > \sqrt{36}\) is true.

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

   • \(\sqrt{49} = 7\)
   • Thus, \(\sqrt{49} > 7\) is false.

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

   • As stated, \(\sqrt{49} = 7\).
   • Thus, \(\sqrt{49} < 7\) is also false.

From these evaluations, the true statements are:

• \(\sqrt{48} > \sqrt{36}\)

So the correct response is:

• \(\sqrt{48} > \sqrt{36}\)