1. **Problem:** Find the diagonal of a cube if each edge is 2. 2. **Formula:** The space diagonal $d$ of a cube with edge length $a$ is given by $$d = a\sqrt{3}$$ because the diagonal spans three edges at right angles. 3. **Calculation:** Given $a=2$, substitute into the formula: $$d = 2\sqrt{3}$$ 4. **Explanation:** We use the Pythagorean theorem in 3D. The diagonal is the hypotenuse of a right triangle whose legs are the face diagonal and the edge. The face diagonal is $a\sqrt{2}$, so the space diagonal is $$\sqrt{(a\sqrt{2})^2 + a^2} = \sqrt{2a^2 + a^2} = \sqrt{3a^2} = a\sqrt{3}$$. 5. **Final answer:** The diagonal of the cube is $$2\sqrt{3}$$.