1. **Problem statement:** We have a right triangle with one leg of length 8 and a hypotenuse of length $2\sqrt{41}$. We need to find the length of the other leg. 2. **Formula used:** In a right triangle, the Pythagorean theorem states: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse, and $a$ and $b$ are the legs. 3. **Assign known values:** Let the unknown leg be $x$. Then: $$8^2 + x^2 = (2\sqrt{41})^2$$ 4. **Calculate squares:** $$64 + x^2 = 4 \times 41$$ $$64 + x^2 = 164$$ 5. **Isolate $x^2$:** $$x^2 = 164 - 64$$ $$x^2 = 100$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{100}$$ $$x = 10$$ 7. **Answer:** The length of the third side is $10$. This is already in simplest radical form since it is an integer.