Any person desiring to do any plumbing, or to work at the business of plumbing, in any city or village which has established a plumbing board, shall make written application to the plumbing board for examination for a license, which examination shall be made at the next meeting of the plumbing board, or at an adjourned meeting. The plumbing board shall examine the applicant as to his or her practical knowledge of plumbing, house drainage, ventilation, and sanitation, which examination shall be practical as well as theoretical, and if the applicant has shown himself or herself competent, the plumbing board shall cause its chairperson and secretary to execute and deliver to the applicant a license authorizing him or her to do plumbing in such city or village and also within the area of extraterritorial zoning jurisdiction of cities of the metropolitan class.