It has been suggested that for liquids s3 beta4=  K, is a constant, with s being the surface tension and  the compressibility, show that K is not a dimensionless constant.

Dear student,

Surface tension is force per unit length.Dimension of Force is $M^1{L}^1{T}^{-2}$,divided by length we get the dimensional formula of surface tension is $M^1{L}^0{T}^{-2}$.
Compressibility is the fractional change in volume per unit increase in pressure.Dimension of compressibility is $M^{-1}{L}^1{T}^2$.
$$\begin{gathered} \left[S\right]=M^1{L}^0{T}^{-2} \\ \left[\beta \right]=M^{-1}{L}^1{T}^2 \\ {S}^3{\beta }^4=K \\ \left[M^3{L}^0{T}^{-6}{M}^{-4}{L}^4{T}^8\right]=K \\ K=M^{-1}{L}^4{T}^2 \end{gathered}$$

K is not a dimensionless constant.

Regards.