The board shall ______ any place of business at reasonable hours.

The correct answer is "inspect" because under Tennessee cosmetology laws, the governing board is responsible for ensuring that all cosmetology establishments are operating in compliance with the laws and regulations set forth by the state. This involves conducting inspections of places of business at reasonable hours to assess their adherence to health and safety standards, facility cleanliness, and the proper licensing of practitioners. Regular inspections help maintain industry integrity and protect public health and safety.

The other options—evaluate, regulate, and approve—do not specifically align with the formal responsibilities entailed in the inspection process. While evaluating and regulating may be part of the broader oversight functions of the board, the term "inspect" directly refers to the action of examining a business's conditions. Approving implies giving permission or endorsing an establishment, which is a different function from the proactive measure of inspecting a location to ensure it meets required standards.