Question 27
Find the integer that is closest to the value of the expression:
$$
\left( (3 + \sqrt{1})^{2023} - \left( \frac{1}{3 - \sqrt{1}} \right)^{2023} \right) \cdot \left( (3 + \sqrt{2})^{2023} - \left( \frac{1}{3 - \sqrt{2}} \right)^{2023} \right) \cdot \left( (3 + \sqrt{3})^{2023} - \left( \frac{1}{3 - \sqrt{3}} \right)^{2023} \right) \dots \left( (3 + \sqrt{8})^{2023} - \left( \frac{1}{3 - \sqrt{8}} \right)^{2023} \right).
$$
$$
\left( (3 + \sqrt{1})^{2023} - \left( \frac{1}{3 - \sqrt{1}} \right)^{2023} \right) \cdot \left( (3 + \sqrt{2})^{2023} - \left( \frac{1}{3 - \sqrt{2}} \right)^{2023} \right) \cdot \left( (3 + \sqrt{3})^{2023} - \left( \frac{1}{3 - \sqrt{3}} \right)^{2023} \right) \dots \left( (3 + \sqrt{8})^{2023} - \left( \frac{1}{3 - \sqrt{8}} \right)^{2023} \right).
$$