Approximate Values of Irrational Numbers Quick Check

Question

3 of 53 of 5 Items
Question
Using rational approximations, what statement is true?(1 point)
Responses

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

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

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

49−−√>7

Answer 1

To determine which statements about the square roots are true, let's evaluate each one:

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

   • \(\sqrt{36} = 6\)
   • \(\sqrt{48} \approx 6.93\) (since \(48\) is between \(36\) and \(64\))
   • This statement is true.

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

   • This is the opposite of the first statement, which we found to be true, so this is false.

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

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

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

   • Similarly, this is the opposite of the third statement, so this is also false.

Based on this evaluation, the true statement is:

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