Europeans began establishing colonies in north america. what year did this happen?

It happened in 1607.

Explanation:

The first colony was established at Jamestown, Virginia, in 1607. A lot of people settled in the New World escaping religious persecution. The Pilgrims arrived in 1620. and founded Plymouth, Massachusetts. In both Virginia and Massachusetts, the colonists had some kind of, we could say support from Native Americans.        

European Nations established colonies in North America because they wanted to expand their horizons (main reasons were the gold, glory, and spreading their religion). They also wanted to have more land than other countries.

The Spanish were among the first Europeans to explore the New World and the first to settle in what is now the United States.

By 1650, England had established a dominant presence on the Atlantic coast. They discovered corn which kept them from starving while, in Virginia, tobacco was a great way to make money. In early 1700s enslaved Africans contributed a growing percentage of the colonial population. By 1770, more than 2.000.000 people lived and worked in Great Britain's 13 North American colonies.