a) (i) To find the mean of the measurements:
Compute:
\( \text{Mean} = \frac{5.96 + 5.95 + 6.02 + 5.95 + 5.99}{5} = 5.974 \)

Thus:
The mean is \( 5.974 \).

a) (ii) To calculate the percentage error:
Use the formula:
\( \text{% error} = \frac{|6 – 5.974|}{5.974} \times 100\% \)
Compute:
\( \text{% error} = \frac{0.026}{5.974} \times 100\% \approx 0.435\% \)

Thus:
The percentage error is \( 0.435\% \).

b) To calculate \( \sqrt{3.87^5 – 8.73^{-0.5}} \):
Compute the expression:
\( 3.87^5 \approx 3452.59208024 \)
\( 8.73^{-0.5} = \frac{1}{\sqrt{8.73}} \approx 0.338505098 \)
\( 3.87^5 – 8.73^{-0.5} \approx 3452.59208024 – 0.338505098 = 3452.25357514 \)
\( \sqrt{3452.25357514} \approx 29.45728613 \)

(i) Round to the nearest integer:
\( 29.45728613 \approx 29 \)

Thus:
The answer is 29.

(ii) Express in the form \( a \times 10^k \):
\( 29.45728613 = 2.945728613 \times 10^1 \approx 2.95 \times 10^1 \)

Thus:
The answer is \( 2.95 \times 10^1 \).