Answer is 11 using only four 4's?

(4/.4) + (4/4)

Another way if you are not allowed to use 0.4 (which I wasn't when I did this)

is (sigma index = square root of 4 maximum value of 4

( i )) +4-square root of 4 this comes out to... 2+3+4+4-2 or 3+4+4 which = 11