In a lab we used distilled water + 3 drops of soap to examine how beetroot would be affected by it. I believe the beetroots membrane denatured and a red pigment leaked from it. However, I cannot explain why this has happened. Can anyone explain the topic question to me?
@mdperry answered well. If you need some diagrams to help with understanding, this article Should be helpful.
As you surmised, when you add detergent, it is lysing some cells of the beetroot that contain pigment. That pigment then gets released into solution. I've annotated the image below for the micelles that gets formed, except I spelled it wrong :/