Lets look at the following example.

    Ordering[{0, 20 Sqrt[5], 40 Sqrt[5], 20 Sqrt[5], 20 Sqrt[10]} // N]
    
which gives the right answer

>     {1, 2, 4, 5, 3}

but if one removes the `N` one gets the wrong answer

    Ordering[{0, 20 Sqrt[5], 40 Sqrt[5], 20 Sqrt[5], 20 Sqrt[10]}]
>     {1, 2, 4, 3, 5}

Is it a bug?