Re: How and why more beetroot pigment is relesed in different conc. of detergnt

The pigments in beetroot are called betalaines and are found in all plants 
belonging to a taxonomic group known as "Caryophyllales". There they replace the 
xantophylles as pigments found in the vacuole and have a color-span from yellow 
to orange. In contrast to the xantophylles they do not show a pH-dependent change 
of color.

The amount of pigment extracted from beetroot pieces is only indirectly dependent 
on the concentration of detergent in the solution you use. Detergents help bring 
fat and lipids into solution. For this reason they are used in many biochemical 
methods to help break down membranes. In your experiment higher detergent 
concentration leads to a more efficient membrane destruction, opening more 
vacuoles and so setting free more pigment.

Information on this can be found in every biochemistry textbook ("Biochemistry", 
Stryer) and most chemistry textbooks.