a, (2sqrt{6}-4sqrt{3}+5sqrt{2}-1/4 sqrt{8}).3sqrt{6}
= 2sqrt{6}.3sqrt{6}-4sqrt{3}.3sqrt{6}+5sqrt{2}.3sqrt{6}-1/4 .sqrt{8}.3sqrt{6}
= 36-36sqrt{2}+30sqrt{3}-3sqrt{3}
=36-36sqrt{2}+27sqrt{3}
b, 2sqrt{2}(2-3sqrt{3})+(1-2sqrt{2})^2+6sqrt{6}
= 4sqrt{2}-6sqrt{6}+6sqrt{6}+1+8-4sqrt{2}
= 9
c, 20(sqrt{300}-15sqrt{675}+5sqrt{75}):sqrt{15}}
= 20(sqrt{300}:sqrt{15}-15sqrt{675}:sqrt{15}+5sqrt{75}:sqrt{15})
= 20(2sqrt{5}-45sqrt{5}+5sqrt{5})
=20. (-38)sqrt{5} = -760sqrt{5}
