To solve the equation \( z^2 = 109.434613210000 \), we need to take the square root of both sides.
- Calculate the square root:
\[ z = \sqrt{109.434613210000} \]
- Using a calculator, we find:
\[ z \approx 10.463 \]
- We will round this to the nearest tenth:
\[ z \approx 10.5 \]
Thus, the final answer is:
\[ z \approx 10.5 \]