Question 1039237
Let A, B, C be the numbers.

==> {{{sqrt(AB) = sqrt(A*Ar) = sqrt(A^2*r) = A*sqrt(r)=6}}}, and 

 {{{sqrt(BC) = sqrt(Ar*Ar^2) = sqrt(A^2*r^3) = A*sqrt(r^3)=24}}}.

==> {{{(A*sqrt(r^3))/(A*sqrt(r))= r = 24/6 = 4}}}

==> {{{A*sqrt(4) = 6}}}  ==> {{{highlight(A = 3)}}}.

==> {{{B = 3*4 = highlight(12)}}},

==> {{{C = 12*4 = highlight(48)}}}.