And the second one does not count then ? And the second is extermination according to my eyes.
Do you know why in the dictionary it's a second preference? BECAUSE IT'S NOT FIRST.
Seriously, pay attention to what has been posted.
Langenscheidt's German-English, English-German Dictionary from 1942 lists under "ausrotten": "root out; extirpate; exterminate." Exterminate being the third option.
Soon after the Germans entered Poland, they began mass evictions of Poles from the provinces of Western Poland. They expelled by force large numbers of landowners and of the richer peasants, of industrialists, merchants, craftsmen, lawyers, teachers and doctors.
The mass evictions from the incorporated territories assumed gigantic proportions. According to approximate estimates, by March 1, 1940, the Germans had removed about 1000000 people from Western Poland, and by the end of August their number must have reached over 1500000. This terrifying figure almost staggers the imagination. These million and a half have been robbed of all their property. They were expelled mostly during the severe winter of last year from their homes, so giving the full sense to the peculiarly German word "ausrotten" (exterminate and extirpate). The fate of these involuntary refugees was tragic. Robbed of all they possessed, they were forced to leave their homes, their farms and workshops at a few hours' notice. Trains of unheated cattle trucks — even during the severest frosts of the winter — carried them far from the frontiers of the incorporated provinces, and after many days of travel, during which numerous men, women and children died of hunger and cold, they were abandoned, hungry, cold and in rags, on the territory of the Gouvernement-General, itself ravaged by the war.
Source: Poland After One Year of War, Published for the Polish Ministry of Information by G. Allen and Unwin limited, 1940, pages 39-41
A later move of the Nazis in their effort to ausrotten, root out, the Jews was the heartless deportation on a moment's notice of thousands of older Jews from the Rhineland to évacué camps in Southern France, where indescribable hardships brought death to hundreds.
Source: The Jews Today: A Call to Christian Action, Conrad Hoffman, 1941, page 6
The overt aim of the government was to annihilate Polish landed property, and in consequence uproot the Polish population itself, according to the motto of the philosopher Edward Hartmann : « ausrotten ». The names of towns and villages were germanized; Polish schoolmasters and functionaries transferred to the most distant parts of Prussia; the Germans who did not show enough zeal in the work of germanization had the same fate.
Source: A Brief Outline of Polish History, Władysław Konopczyński, 1920, page 80
Frau X. turned on the radio to Berlin, and upon our horrified ears fell the frenzied accents of the Fuehrer, announcing his instant resolve to root out the Poles. "Ich bin fest entschlossen die Polen auszurotten. Sieg heil! Sieg heil!"
Source: The Scots Magazine, 1939, page 123
In these expulsions one aim is discernible, to uproot the Jew as much as possible, to turn him more and more into a homeless wanderer, into a beggar. If the Jew remains in his old place, he manages to get around all the bans and restrictions. He then finds friends and supporters even among the non-Jewish population who help him find a way to earn a little, to obtain a morsel of bread, and once in a while to get some butter or cheese. Away from home, he is more helpless, more readily doomed to hunger and want, and hence nearer to destruction, which is the real object of all the persecutions and oppressions, of all the discriminatory laws and regulations.
Source: Jews in Nazi Europe, February 1933 to November 1941: a study prepared by the Institute of Jewish affairs, submitted to the Inter-American Jewish conference, November 23-24-25, 1941, Baltimore, Md
From the towns and counties of Wloclawek, Sieradz, Plock, Wielun and others, 50000 to 60000 Jews were uprooted. There were towns from which the entire Jewish population was ordered to leave. Always they were given only short notice. They could take with them a small provision of food and their most necessary personal belongings.
Source: Hitler's ten-year war on the Jews, Institute of Jewish Affairs of the American Jewish Congress, World Jewish congress, 1943, page 139
"After less than a generation, even the remaining ones were uprooted out of this land, sold and scattered all over the world."
Nach weniger als Einem Menschenalter wurden auch noch die übrigen ausgerottet aus diesem Lande, verkauft, zerstreut in alle Welt.
Source: Geschichte der Religion Jesu Christi, Friedrich Leopold, volume 2, 1818, page 93
"butchered and rooted out millions of its leading intelligentsia with savage blood-lust "
[...] Millionen seiner führenden Intelligenz in wilder Blutgier abwürgte und ausrottete [...]
Source: Adolf Hitler, Mein Kampf, 1936, page 750
During a conversation on July 4th, 1942, with Czech president Emil Hácha, Hitler threatened with the expulsion of Czechs from Bohemia and Moravia. Hácha stated that "as the basis of their future policy," they will stamp out (ausrotten) all persons advocating pro-Soviet (Edvard Beneš) policy, i.e. remove from their positions.
Source: Hitler's Table Talk, any version, memo for July 4th, 1942
Here's another quote, from a 2008 exhibition in the Digital Archives of Marburg, from a yet unfinished publication called "Die Verfolgung der Sinti und Roma in Hessen von der frühen Neuzeit bis nach dem II. Weltkrieg" by Dr. Udo Engbring-Romang:
Mit dem Mittel der guten „Policey“ sollten schließlich die „Zigeuner" beseitigt oder "ausgerottet" werden, das heißt ihre Rotte, ihr Gruppenzusammenhalt, sollte zerstört werden. In Einzelfällen war der Begriff der „Ausrottung“ auch als Eliminierung der Individuen verstanden worden.
Here's from his 2006 publication, "Antiziganismus: Begriff, Idee, Funktion und Umsetzung:"
Mit dem Mittel der guten „Policey“ sollten schließlich die „Zigeuner ausgerottet“ werden, das heißt ihre Rotte, ihr Gruppenzusammenhalt, sollte zerstört werden. [no "In Einzelfällen..." this time]