Using rational approximations, what statement is true?

Question

√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: \[ \sqrt{12} > \pi \]