this is more to do with mathematics than physics,
but the square root of gravity on its own means nothing, its simply a acceleration due to gravity near the earth surface.
trying to find the speed of a falling object is a simple conservation of energy problem, then it has a meaning in that context.
however standing alone, it has no bearing to the real world. it is simply a mathematical term or construct we use in order to explain the real world. you see this all over the place in physics, you just have to get used to it.
for example:
mv^2=mhg
v^2=gh
v= SQRT(gh)
=SQRT(g)SQRT(h)
so SQRT means nothing on its own, simply a mathematical term to used to calculate the effects and actions in the real world.
i cant really compare it to Pi, sorry
but i hope you have a better understanding :)
