[tex] \sqrt{6+2 \sqrt{5} } - \sqrt{5} = \\ \\
= \sqrt{5+1 +2 \sqrt{5} } - \sqrt{5} = \\ \\
= \sqrt{5 +2 \sqrt{5} +1} - \sqrt{5} = \\ \\
= \sqrt{\Big(\sqrt5\Big)^2 +2 \times \sqrt{5}\times 1 +1^2} - \sqrt{5} = \\ \\
= \sqrt{\Big(\sqrt5+1\Big)^2} - \sqrt{5} = \underline{\sqrt5}+1 - \underline{\sqrt{5} } = \boxed{1} \in N \subset Q
[/tex]
