Question

Using rational approximations, what statement is true?

√12> π

√12<π

√ 16 > 4

√16 < 4

Answer 1

To evaluate the statements using rational approximations, we first need to determine the values of each expression.

1. **Calculating √12:**
\[
\sqrt{12} \approx 3.464
\]

2. **Calculating π:**
Using the approximate value of π:
\[
\pi \approx 3.142
\]

Now let's compare:
- \(\sqrt{12} \approx 3.464\) and \(\pi \approx 3.142\), therefore:
\[
\sqrt{12} > \pi
\]

3. **Calculating √16:**
\[
\sqrt{16} = 4
\]

Now let's compare:
- \(\sqrt{16} = 4\), thus:
\[
\sqrt{16} = 4
\]
which means that both \( \sqrt{16} > 4 \) and \( \sqrt{16} < 4 \) are false.

Based on these calculations, the only true statement among the ones provided is:
\[
\sqrt{12} > \pi
\]