Go to your YouTube app and start a video. Then close it out. The video will stop, so next you have to hit the Home button twice (or do the four finger swipe up move) to reveal the multitasking bar. Then swipe to the right to bring the leftmost page to the front. The YouTube icon should be right there on the right, with the controls. Press play and the YouTube app will start back up again.
Then, you can open Safari and browse.
I just did this process on an iPad running iOS 5.0.1, so it should work on any iPad running that version. I'm assuming it'll work the same for other versions, though I don't know for sure.
Good luck and let us know how you get on.
Marilyn