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?

\(\frac{\sqrt{hG}}{c^{\frac{3}{2}}}\)

[L] = [h^ac^bG^c]

[L] = [ML²T^-1]^a[LT^-1]^b[M^-1L³T^-2]^c

On solving : a = 1/2 ; b = -3/2 ; c = 1/2

L = \(\frac{\sqrt{hG}}{c^{\frac{3}{2}}}\)