The Lightswitch Problem

Imagine 100 light bulbs with light switches numbered 1 through 100, all in a row, all off. Suppose you do the following: toggle all switches that are multiples of 1, then toggle all switches that are multiples of 2, then toggle all switches that are multiples of 3, etc.
By the time you are finished (and have toggled multiples of 100, which is just the last switch), which light bulbs are on and which are off?

See Numberphile.

Here you can experiment and see the outcomes for yourself.