Consider two spheres, each radius r, mass m, density r.
Let the spheres be just touching and held together by mutual gravity F*
F*=Gmm/(2r)2.
Let the two spheres be a distance x from a large sphere of radius R, mass M, density r.
The three spheres are in a line so the attraction by M on the nearer sphere Fn is
Fn=GMm/(x-r)2
and on the more distant small sphere Ff is a bit less,
Ff=GMm/(x+r)2.
For x>>r we have
Fn-Fr=dF/dx=2GMm/x3
and setting F*=dF with dx=2r (attraction=tidal disruption) we get
Gmm/4r2=2GMm(2r)/x3
or
x3=16(M/m)r3.
And now a beautiful thing happens if all the densities are the same,
M/m=V/v=R3/r3
so we get x=2.52R
Which compares with the Roche limit x=2.44R.
Typical comet densities are a fifth that of the Earth so we might expect the limit to be the cube root of five (=1.7) greater or x~4R so by the time a comet approaches 25,000 km (from the Earth's centre) it should start to break up.