6)$(\sqrt[]{2}+2)\sqrt[]{2}-2\sqrt[]{2}$
= $\sqrt[]{2}(\sqrt[]{2}+2-2)$
= $\sqrt[]{2}.\sqrt[]{2}$
= $2$
8) $\sqrt[]{(1-\sqrt[]{2})^2}+\sqrt[]{(\sqrt[]{2}+3)^2}$
= $|1-\sqrt[]{2}|+|\sqrt[]{2}+3|$
= $\sqrt[]{2}-1+\sqrt[]{2}+3$(vì $1-\sqrt[]{2}<0)$
= $2\sqrt[]{2}+2$
= $2(\sqrt[]{2}+1)$