The difference between Barrack and Root for

Barrack as a noun (military, chiefly, in the plural):

A building for soldiers, especially within a garrison; originally referred to temporary huts, now usually to a permanent structure or set of buildings.

Barrack as a noun (chiefly, in the plural):

primitive structure resembling a long shed or barn for (usually temporary) housing or other purposes

Barrack as a noun (chiefly, in the plural):

any very plain, monotonous, or ugly large building

Barrack as a noun (US, regional):

A movable roof sliding on four posts, to cover hay, straw, etc.

Barrack as a noun (Ireland, colloquial, usually, in the plural):

A police station.

Barrack as a verb (transitive):

To house military personnel; to quarter.

Barrack as a verb (intransitive):

To live in barracks.

Barrack as a verb (British, transitive):

To jeer and heckle; to attempt to disconcert by verbal means.

Barrack as a verb (Australia, New Zealand, intransitive):

To cheer for or support a team.

Root for as a verb (transitive, informal):

To encourage (a favored person, team, or result).