To solve the equation \( z^2 = 109.434613210000 \), you need to take the square root of both sides.
The solution is given by:
\[ z = \sqrt{109.434613210000} \]
Calculating this:
\[ z = 10.45947837\ldots \]
Rounding to the nearest tenth, we have:
\[ z \approx 10.5 \]
Therefore, the final answer is:
\[ z \approx 10.5 \]