Using dimensional analysis (and The Buckingham PI Theorem), you can approximate the Planck length, from:
f(Lp, c, G, h) = 0
(Lp being the Planck length, and the other 3 being the obvious.)
The result being: Lp = k.sqrt(Gh/c³) ~ 10^-35 m.
My questions though:
1- How can you justify the assumption that Lp depends on c, G, and h?
2- Why not include eps_0 (permittivity of free space), and e (elementary charge)? They are surely equally fundamental?