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

Question

Responses

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

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

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

12 −−−√ >π

Answer 1

To determine which of the given statements is true, we can evaluate each one:

1. \(\sqrt{16} > 4\)
   \(\sqrt{16} = 4\)
   Therefore, this statement is false.

2. \(\sqrt{16} < 4\)
   As previously established, \(\sqrt{16} = 4\).
   Therefore, this statement is false.

3. \(\sqrt{12} < \pi\)
   To approximate, \(\sqrt{12} \approx 3.464\) and \(\pi \approx 3.14159\).
   Here, \(\sqrt{12} > 3.14 < \pi\), so this statement is true.

4. \(\sqrt{12} > \pi\)
   Given the approximation from the previous point, we see that \(\sqrt{12} \approx 3.464 > 3.14159 \approx \pi\), so this statement is false.

Based on the evaluations, the true statement is:

\(\sqrt{12} < \pi\)