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

Question

Responses

16−−√>4
start root 16 end root greater than 4

12 −−−√<π
start root 12 end root less than pi

16 −−−√<4
start root 16 end root less than 4

12 −−−√ >π
start root 12 end root greater than pi

Answer 1

To evaluate the statements using rational approximations, let's analyze each one:

1. \(\sqrt{16} > 4\):

   • \(\sqrt{16} = 4\), so this statement is false.

2. \(\sqrt{12} < \pi\):

   • \(\sqrt{12} \approx 3.464\) and \(\pi \approx 3.142\), so this statement is also false (\(\sqrt{12} > \pi\)).

3. \(\sqrt{16} < 4\):

   • As mentioned, \(\sqrt{16} = 4\), so this statement is false.

4. \(\sqrt{12} > \pi\):

   • We established that \(\sqrt{12} \approx 3.464\) and \(\pi \approx 3.142\), so this is true.

Thus, the true statement is \(\sqrt{12} > \pi\).