`a)`

`E=[7/(sqrt(2)-1)+56/(sqrt(2)-4)+3/(sqrt(3)+sqrt(2))]:sqrt(12-6sqrt(3))`

`=[(7(sqrt(2)+1))/(2-1)+(56(sqrt(2)+4))/(2-16)+(3(sqrt(3)-sqrt(2)))/(3-2)]:sqrt((3-sqrt(3))^2)`

`=[(7(sqrt(2)+1))/1+(56(sqrt(2)+4))/(-14)+(3(sqrt(3)-sqrt(2)))/1]:(3-sqrt(3))`

`=[7(sqrt(2)+1)-4(sqrt(2)+4)+3(sqrt(3)-sqrt(2))]:(3-sqrt(3))`

`=(7sqrt(2)+7-4sqrt(2)-16+3sqrt(3)-3sqrt(2)):(3-sqrt(3))`

`=(3sqrt(3)-9):(3-sqrt(3))`

`=(-3(3-sqrt(3))):(3-sqrt(3))`

`=-3`

Vậy `E=-3`

`b)`

`F=[8/(sqrt(3)-1)-4/(sqrt(3)+1)+4/(sqrt(5)+sqrt(3))]:sqrt(14+6sqrt(5))`

`=[(8(sqrt(3)+1))/(3-1)-(4(sqrt(3)-1))/(3-1)+(4(sqrt(5)-sqrt(3)))/(5-3)]:sqrt((3+sqrt(5))^2)`

`=[(8(sqrt(3)+1))/2-(4(sqrt(3)-1))/2+(4(sqrt(5)-sqrt(3)))/2]:(3+sqrt(5))`

`=[4(sqrt(3)+1)-2(sqrt(3)-1)+2(sqrt(5)-sqrt(3))]:(3+sqrt(5))`

`=(4sqrt(3)+4-2sqrt(3)+2+2sqrt(5)-2sqrt(3)):(3+sqrt(5))`

`=(6+2sqrt(5)):(3+sqrt(5))`

`=[2(3+sqrt(5))]:(3+sqrt(5))`

`=2`

Vậy `F=2`

`c)`

`G=1/sqrt(4-2sqrt(3))-1/sqrt(7-sqrt(48))+3/sqrt(12-6sqrt(3))`

`=1/sqrt((sqrt(3)-1)^2)-1/sqrt((2-sqrt(3))^2)+3/sqrt((3-sqrt(3))^2)`

`=1/(sqrt(3)-1)-1/(2-sqrt(3))+3/(3-sqrt(3))`

`=(sqrt(3)+1)/(3-1)-(2+sqrt(3))/(4-3)+(3(3+sqrt(3)))/(9-3)`

`=(sqrt(3)+1)/2-(2+sqrt(3))+(3(3+sqrt(3)))/6`

`=(sqrt(3)+1)/2-(2+sqrt(3))+(3+sqrt(3))/2`

`=(sqrt(3)+1+3+sqrt(3))/2-2-sqrt(3)`

`=(4+2sqrt(3))/2-2-sqrt(3)`

`=2+sqrt(3)-2-sqrt(3)`

`=0`

Vậy `G=0`

`d)`

`H=[((sqrt(3)-sqrt(2))^2+4sqrt(6))/(sqrt(3)+sqrt(2))^2].(sqrt(3)-sqrt(2))`

`=(3-2sqrt(6)+2+4sqrt(6))/(sqrt(3)+sqrt(2))^2.(sqrt(3)-sqrt(2))`

`=(5+2sqrt(6))/(sqrt(3)+sqrt(2))^2 .(sqrt(3)-sqrt(2))`

`=(sqrt(3)+sqrt(2))^2/(sqrt(3)+sqrt(2))^2 .(sqrt(3)-sqrt(2))`

`=1.(sqrt(3)-sqrt(2))`

`=sqrt(3)-sqrt(2)`

Vậy `H=sqrt(3)-sqrt(2)`