Let the physical quantity with dimension of length $L$ be related to $h$, $c$, and $G$ as: $L \propto h^x c^y G^z$ Substituting the dimensions of each quantity: Dimension of Planck's constant, $h = [M L^2 T^{-1}]$ Dimension of speed of light, $c = [L T^{-1}]$ Dimension of universal gravitational constant, $G = [M^{-1} L^3 T^{-2}]$

$[L^1] = [M L^2 T^{-1}]^x [L T^{-1}]^y [M^{-1} L^3 T^{-2}]^z$ $[M^0 L^1 T^0] = [M^{x-z} L^{2x+y+3z} T^{-x-y-2z}]$ Equating the powers of $M$, $L$, and $T$ on both sides, we get: For $M$: $x - z = 0 \implies x = z$ For $T$: $-x - y - 2z = 0 \implies -z - y - 2z = 0 \implies y = -3z$ For $L$: $2x + y + 3z = 1 \implies 2z + (-3z) + 3z = 1 \implies 2z = 1 \implies z = 1/2$

Since $z = 1/2$, we have $x = 1/2$ and $y = -3/2$. Therefore, the combination having the dimensions of length is $h^{1/2} c^{-3/2} G^{1/2} = \frac{\sqrt{hG}}{c^{3/2}}$.