You can listen to YouTube music videos and browse the web, use another app or play games at the same time. Here’s how to do it:
Steps:
1.Launch Safari on your iPad, iPhone or iPod touch and visit youtube.com. Note that this trick will not work if you use the YouTube app.
2.Search for a video that you want to listen to in the background. Play any of your favorite song / video. It is important that you start playing the YouTube video before step 3.
3.Press the home button. Note that YouTube (audio) will quit playing.
4.Swipe up from the bottom of the screen to open the Control Center and tap the Play button to continue playing only the audio from the YouTube video.
5.Now You can play YouTube videos in the background and hear the YouTube audio. Open another app, or browse the web (another tab than youtube.com tab), write emails etc .
More: How to listen YouTube while using other apps on iPad/iPhone/iPod Touch