To determine the mean of \(\sqrt{3}\), \(\sqrt{12}\), \(\sqrt{48}\), and \(\sqrt{75}\), follow these steps:
1. Calculate the Square Roots:
- \(\sqrt{3} \approx 1.7320508075688772\)
- \(\sqrt{12} \approx 3.4641016151377544\)
- \(\sqrt{48} \approx 6.928203230275509\)
- \(\sqrt{75} \approx 8.660254037844387\)
2. Sum the Values:
[tex]\[
1.7320508075688772 + 3.4641016151377544 + 6.928203230275509 + 8.660254037844387 = 20.784609690826528
\][/tex]
3. Calculate the Mean:
[tex]\[
\text{Mean} = \frac{\text{Total Sum}}{\text{Number of Values}} = \frac{20.784609690826528}{4} = 5.196152422706632
\][/tex]
4. Express the Mean in Terms of \(\sqrt{3}\):
We observe that the mean value calculated \(5.196152422706632\) can be expressed as \(3 \sqrt{3} \approx 5.196152422706632\).
Thus, the correct answer to the problem is:
[tex]\[
\boxed{3 \sqrt{3}}
\][/tex]
