Question

Using rational approximations, what statement is true?(1 point) Responses 16−−√>4 start root 16 end root greater than 4 12 −−−√ >π start root 12 end root greater than pi 16 −−−√<4 start root 16 end root less than 4 12 −−−√<π

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 \(\pi \approx 3.142\). Therefore, this statement is **true**.

3. **\(\sqrt{16} < 4\):**
As established before, \(\sqrt{16} = 4\). So this statement is **false**.

4. **\(\sqrt{12} < \pi\):**
Since \(\sqrt{12} \approx 3.464\) and \(\pi \approx 3.142\), this statement is also **false**.

Thus, the true statement is:
\[
\sqrt{12} > \pi.
\]