√(11-4√7)
=√(7-4√7+4)
=√(√7-2)²
=√7-2
√(16-4√7)
=√(9-4√7+7)
=√(3-√7)²
=3-√7
所以
原式
=(√7-2+3-√7)^2008
=1^2008
=1