1. **Problem:** Find the unknown side length $c$ of a right triangle with legs $a=2$ and $b=3$. 2. **Formula:** Use the Pythagorean theorem: $$c^2 = a^2 + b^2$$ 3. **Calculation:** $$c^2 = 2^2 + 3^2$$ $$c^2 = 4 + 9$$ $$c^2 = 13$$ 4. **Solution:** $$c = \sqrt{13}$$ 5. **Explanation:** The hypotenuse $c$ is the square root of the sum of the squares of the legs. Here, it is left as the radical $\sqrt{13}$ as requested. **Final answer:** $c = \sqrt{13}$