To determine which statement is true, we need to approximate the values of [tex]\(\sqrt{12}\)[/tex], [tex]\(\pi\)[/tex], and [tex]\(\sqrt{16}\)[/tex], and then compare them.
Let's start with [tex]\(\sqrt{12}\)[/tex] and [tex]\(\sqrt{16}\)[/tex]:
- [tex]\(\sqrt{12} \approx 3.4641\)[/tex]
- [tex]\(\sqrt{16} = 4\)[/tex]
Next, recall the value of [tex]\(\pi\)[/tex]:
- [tex]\(\pi \approx 3.1416\)[/tex]
Now, let's evaluate each of the given inequalities:
1. [tex]\(\sqrt{12} < \pi\)[/tex]
- [tex]\(\sqrt{12} \approx 3.4641\)[/tex] is not less than [tex]\(\pi \approx 3.1416\)[/tex].
- This statement is False.
2. [tex]\(\sqrt{16} > 4\)[/tex]
- [tex]\(\sqrt{16} = 4\)[/tex] is not greater than 4.
- This statement is False.
3. [tex]\(\sqrt{12} > \pi\)[/tex]
- [tex]\(\sqrt{12} \approx 3.4641\)[/tex] is indeed greater than [tex]\(\pi \approx 3.1416\)[/tex].
- This statement is True.
4. [tex]\(\sqrt{16} < 4\)[/tex]
- [tex]\(\sqrt{16} = 4\)[/tex] is not less than 4.
- This statement is False.
After evaluating each of the statements, we find that the true statement is:
[tex]\[
\sqrt{12} > \pi
\][/tex]
