I'd say "три белые тарелки" and "три белых тарелки" are both possible.
Numerals employ some rules of noun agreement, as it was already discussed here: A small question about много.
Basically, there are three forms depending on the last numeric word (examples are given for masculine, feminine and neuter):
один стол, одно окно, одна тарелка (... один);
два стола, два окна, две тарелки (... два/три/четыре);
пять столов, пять окон, пять тарелок (... anything except один/два/три/четыре).

When they combine with adjectives, there are some tricks however. In most of cases, the adjective takes the same form as the noun:
один белый стол, одно белое окно, одна белая тарелка;
пять белых столов, пять белых окон, пять белых тарелок.

However, the second form (genitive singular) is more tricky. The adjective takes genitive plural while the noun is in singular:
два белых стола, два белых окна, две белых тарелки.

Finally, if the noun is feminine, it can often take nominative plural: две белые тарелки = две белых тарелки. This is only true for feminine nouns. For masculine and neuter, only one form is possible.

This seeming disagreement has developed from the old Russian dual form, which ceased to exist by merging into other similar-sounding forms.