There is no research that suggests dirty hair grows faster than clean hair. The hair must be washed regularly to maintain a healthy scalp.
Women often think that dirty hair grows faster because they do less to it, resulting in less breakage. Less breakage helps the hair appear healthier and can give the illusion of faster growth.
To maintain a healthy scalp and healthy hair, the hair should be washed every two to three days. Washing hair every day will lead to stripped color, less manageability and hair that is dry and stripped of its natural oils. Washing hair less frequently also helps color last longer.
In between shampoos, using a dry shampoo can make the hair look fresh and help to absorb oil that makes the hair look dirty.