Question

check the dimensional consistency of escape velocity v = sq root of 2GM/R

Answer 1

For dimensional consistency dimension of left side of equation must be same as the dimension of the right side of the equation

So for the left side the dimension is of velocity

so it is

$v = L^1T^{-1}$

now for the dimension of gravitational constant G is

$G = M^{-1}L^3T^{-2}$

Now the dimension of right side is given as

$\sqrt{\frac{2GM}{R}} = \sqrt{\frac{M^{-1}L^3T^{-2}*M^1}{L}}$

$\sqrt{\frac{2GM}{R}} = \sqrt{L^2T^{-2}} = L^1T^{-1}$

so here dimension of left side of equation is same as right side

so here dimensional consistency hold good

Answer 2

this is your answer hope it helps