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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?

Let's look at the following example.

Ordering[{0, 20 Sqrt[5], 40 Sqrt[5], 20 Sqrt[5], 20 Sqrt[10]} // N]

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?

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?

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?