1. **State the problem:** We have a right triangle with two legs each of length 8, and we need to find the length of the third side (the hypotenuse). 2. **Formula used:** The Pythagorean theorem states that in a right triangle, the square of the hypotenuse $c$ is equal to the sum of the squares of the legs $a$ and $b$: $$c^2 = a^2 + b^2$$ 3. **Apply the formula:** Here, $a = 8$ and $b = 8$, so $$c^2 = 8^2 + 8^2$$ 4. **Calculate the squares:** $$c^2 = 64 + 64 = 128$$ 5. **Find $c$ by taking the square root:** $$c = \sqrt{128}$$ 6. **Simplify the radical:** $$\sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}$$ 7. **Final answer:** The length of the hypotenuse is $$c = 8\sqrt{2}$$ This is the simplest radical form.