Final answer:
The correctness of the escape velocity formula ve = \u221a(2GM/R) is confirmed by dimensional analysis, showing that both sides of the equation have the dimension of velocity [L T^-1].
Step-by-step explanation:
The escape velocity formula ve = \u221a(2GM/R) can be checked for dimensional correctness by analyzing the dimensions of each term in the equation. The left side of the equation has the dimension of velocity, which is [L T-1], where L is length and T is time. The right side of the equation involves a square root, meaning we need the dimensions within the root to form the square of velocity's dimension. G is the gravitational constant with dimensions [M-1 L3 T-2], M is the mass with dimensions [M], and R is the radius with dimensions [L]. Substituting these dimensions in, we get dimensions for the right-hand side as \u221a([M-1 L3 T-2][M][L]) = \u221a([L2 T-2]) = [L T-1], which matches the left side, hence proving the dimensional correctness of the escape velocity formula.