a, $11+6\sqrt2=9+2.3.\sqrt2+2=(3+\sqrt2)^2$
b, $8-2\sqrt7=7-2.\sqrt7.1=(\sqrt7-1)^2$
c, $\sqrt{11+6\sqrt2}+\sqrt{11-6\sqrt2}=\sqrt{9+2.3.\sqrt2+2}+\sqrt{9-2.3.\sqrt2+2}=\sqrt{(3+\sqrt2)^2}+\sqrt{(3-\sqrt2)^2}=|3+\sqrt2|+|3-\sqrt2|=3+\sqrt2+3-\sqrt2=6$
d, $\sqrt{8-2\sqrt7}-\sqrt{8+2\sqrt7}=\sqrt{7-2\sqrt7.1+1}-\sqrt{7+2\sqrt7.1+1}=\sqrt{(\sqrt7-1)^2}-\sqrt{(\sqrt7+1)^2}=\sqrt7-1-\sqrt7-1=-2$
