Question

order this greatest to least
3π,27,√105

Answer 1

To compare the values of \(3\pi\), \(27\), and \(\sqrt{105}\), we can first calculate or approximate their numerical values.

1. **Calculating \(3\pi\)**:
- Using \(\pi \approx 3.14\),
\[
3\pi \approx 3 \times 3.14 \approx 9.42
\]

2. **Calculating \(\sqrt{105}\)**:
- To approximate, note that \(10^2 = 100\) and \(11^2 = 121\), so \(\sqrt{105}\) is between \(10\) and \(11\).
- A closer estimation can be done by calculating \(10.2^2\) and \(10.3^2\):
- \(10.2^2 = 104.04\)
- \(10.3^2 = 106.09\)
- Therefore, \(\sqrt{105} \approx 10.24\).

3. **Comparing the values**:
- \(3\pi \approx 9.42\)
- \(\sqrt{105} \approx 10.24\)
- \(27 = 27\)

Now we order them from greatest to least:
- \(27\)
- \(\sqrt{105} \approx 10.24\)
- \(3\pi \approx 9.42\)

Thus, the final order from greatest to least is:
\[
27, \sqrt{105}, 3\pi
\]