Question

Question

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

12 −−−√<π

Answer 1

Let's evaluate the statements one by one.

1. \(\sqrt{16} > 4\): This is false because \(\sqrt{16} = 4\).

2. \(\sqrt{16} < 4\): This is also false for the same reason; \(\sqrt{16} = 4\).

3. \(\sqrt{12} > \pi\): To evaluate this, we can approximate. \(\sqrt{12} \approx 3.464\) and \(\pi \approx 3.14\), so \(\sqrt{12} > \pi\) is true.

4. \(\sqrt{12} < \pi\): Since \(\sqrt{12} \approx 3.464\) is greater than \(\pi \approx 3.14\), this statement is false.

Thus, the true statement based on rational approximations is:

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