$\sqrt[]{6+2\sqrt[]{5}}$-$\sqrt[]{6-2\sqrt[]{5}}$
`=`$\sqrt[]{5+2\sqrt[]{5}+1}$-$\sqrt[]{5-2\sqrt[]{5}+1}$
`=`$\sqrt[]{(\sqrt[]{5}+1)^2}$-$\sqrt[]{(\sqrt[]{5}-1)^2}$
`=|`$\sqrt[]{5}$`+1|-|`$\sqrt[]{5}$`-1|`
`=`$\sqrt[]{5}$ `+1-` $\sqrt[]{5}$`+1`
`= 2`