1000 roses

Algebra Level 2

Agnis, being the casanova that he is, bought 1000 roses to give out the the girls in his school on Valentines Day. To the first girl, he gave her 1 rose. To each subsequent girl, as he professes his undying like of them, he gave out (strictly) more roses then he did to the previous.

What is the most number of girls that Agnis could give roses to?

Image credit: Wikipedia Frits Hoogesteger
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