Check the dimensional consistency of the relation `upsilon = (1)/(I) sqrt((P)/(rho))` where I is length, `upsilon` is velocity, P is pressure and `rho` is density,

Explanation

The given relation is `upsilon = (1)/(I) sqrt((P)/(rho))`
`LHS = upsilon = LT^(-1) = [M^0 L^1 T^(-1)]`
`RHS = (1)/(I) sqrt((P)/(rho)) = (1)/(L) sqrt((M L^(-1)T^(-2))/(M L^(-3))) = (1)/(L) (LT^(-1)) =[T^(-1)]`
As LHS != RHS, :. The relation is not dimensionally consistent.