因为(11+4√7)=(√7+2)^2,(11-4√7)=(√7-2)^2,
所以√(11+4√7)^3+√(11-4√7)^3
=(11+4√7)*√(11+4√7)+(11-4√7)*√(11-4√7)
=(11+4√7)*(√7+2)+(11-4√7)*(√7-2)
=50+19√7-50+19√7
=38√7.