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

If Planck’s constant (h), velocity of light (c) and universal gravitational constant (G) are the fundamental quantities, assume L = h^x C^y G^z 

Where x, y, z are constants

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

Equating dimensions of fundamental quantities on both the sides

$\begin{array}{rl} & M^0=M^{x-z} x-z=0,x=z\to \left(1\right)\\ & L^1=L^{2x+y+3z}\\ & 1=2x+y+3x\Rightarrow 5x+y=1\to \left(2\right)(x=z)\\ & T^0=T^{-x-y-2z}\\ & 0=x+y+2z\\ & 0=3x+y\\ & y=-3x\to \left(3\right)\end{array}$

Substituting in (2),

$\begin{array}{rl} & 5x-3x=1\\ & x=1/2\\ & z=1/2\\ & y=-3/2\end{array}$

so,  $L=\frac{h^{1/2}{G}^{1/2}}{C^{3/2}}=\frac{\sqrt{hG}}{C^{3/2}}$