Sorting upon the first element of a nested list and show that as numerical values

SortBy[MapAt[N, lst, {All, 1}], First]

{{-2.41421, {{5, 11}, {5, 12}}}, {-1.20711, {{1, 11}, {1, 12}, {2, 11}}}, {-0.414214, {{7, 9}, {7, 10}}}, {-0.207107, {{1, 9}, {1, 10}}}, {0.207107, {{1, 7}, {1, 8}}}}

SortBy[N @* First] @ lst

{{-1 - Sqrt[2], {{5, 11}, {5, 12}}}, {1/2 (-1 - Sqrt[2]), {{1, 11}, {1, 12}, {2, 11}}}, {1 - Sqrt[2], {{7, 9}, {7, 10}}}, {1/2 (1 - Sqrt[2]), {{1, 9}, {1, 10}}}, {1/2 (-1 + Sqrt[2]), {{1, 7}, {1, 8}}}}

list={{1/2 (-1 - Sqrt[2]), {{1, 11}, {1, 12}, {2, 11}}},{-1 - Sqrt[2], {{5, 11}, {5, 12}}},{1/2 (1 - Sqrt[2]), {{1, 9}, {1, 10}}}, {1 - Sqrt[2], {{7, 9}, {7, 10}}},{1/2 (-1 + Sqrt[2]), {{1, 7}, {1, 8}}}}   

SortBy[N@list,First]    

{{-2.41421, {{5., 11.}, {5., 12.}}}, {-1.20711, {{1., 11.}, {1., 12.}, {2., 11.}}}, {-0.414214, {{7., 9.}, {7., 10.}}}, {-0.207107, {{1., 9.}, {1., 10.}}}, {0.207107, {{1., 7.}, {1., 8.}}}}