L varies as the cube of m and inversely as the square root of N. If L is 108. When m is 3 N is 4. Find N when L is 4000 and M is 10

L = kM^3/√N, so L√N/M^3 = k, which is constant.

So you want N such that
4000√N/10^3 = 108√4/3^3
Now finish it off