Planck's constant (h), speed of light in vaccum c and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?

Let dimensions of length $\mathrm{l} \propto {\mathrm{h}}^{\mathrm{x}}{\mathrm{G}}^{\mathrm{y}}{\mathrm{c}}^{\mathrm{z}}$

${\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^0 = {\left({\mathrm{ML}}^2{\mathrm{T}}^{-1}\right)}^{\mathrm{x}}{\left({\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\right)}^{\mathrm{y}}({\mathrm{LT}}^{-1}{)}^{\mathrm{z}}$

$= {\mathrm{M}}^{\mathrm{x}-\mathrm{y}}{\mathrm{L}}^{2\mathrm{x}+3\mathrm{y}+\mathrm{z}}{\mathrm{T}}^{-\mathrm{x}-2\mathrm{y}-\mathrm{z}}$

Equating  dimensions on left and right hand side,

x- y = 0                    

2x+3y+z= 1     

-x-2y-z=0 

 $\Rightarrow \mathrm{x} = \frac{1}{2}; \mathrm{y} = \frac{1}{2}; \mathrm{z} = \frac{-3}{2}$             

    $\Rightarrow \mathrm{l} \propto \frac{\sqrt{\mathrm{hG}}}{{\mathrm{c}}^{{\displaystyle \frac{3}{2}}}}$