$\sqrt{3+2\sqrt{2}}=\sqrt{1+2+2\sqrt{2}}=\sqrt{2+2\sqrt{2}+1}=\sqrt{(\sqrt{2}{)}^2+2\ast <!--\; \ast \; -->1\ast <!--\; \ast \; -->\sqrt{2}+1^2}=\sqrt{(\sqrt{2}+1{)}^2}=|\sqrt{2}+1|=\sqrt{2}+1$

$\sqrt{7+4\sqrt{3}}=\sqrt{4+3+4\sqrt{3}}=\sqrt{4+4\sqrt{3}+3}=\sqrt{2^2+2\ast <!--\; \ast \; -->2\ast <!--\; \ast \; -->\sqrt{3}+(\sqrt{3}{)}^2}=\sqrt{(2+\sqrt{3}{)}^2}=|2+\sqrt{3}|=2+\sqrt{3}$

$\sqrt{11+2\sqrt{30}}=\sqrt{5+6+2\sqrt{30}}=\sqrt{5+2\sqrt{30}+6}=\sqrt{(\sqrt{5}{)}^2+2\sqrt{5\ast <!--\; \ast \; -->6}+(\sqrt{6}{)}^2}=\sqrt{(\sqrt{5}+\sqrt{6}{)}^2}=|\sqrt{5}+\sqrt{6}|=\sqrt{5}+\sqrt{6}$