12. The mean of [tex] \sqrt{3}, \sqrt{12}, \sqrt{48}, [/tex] and [tex] \sqrt{75} [/tex] is:

a. [tex] 4 \sqrt{3} [/tex]

b. [tex] 3 \sqrt{3} [/tex]

c. [tex] 2 \sqrt{3} [/tex]



Answer :

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]