Which verb means to use formal steps to obtain a required result?

The correct choice indicates the verb that means to use formal steps to obtain a required result. In this context, "prove" is the term that aligns with the idea of systematically demonstrating or establishing the truth or validity of a statement, theory, or hypothesis through a structured process. Proving often involves rigorous methodologies or procedures, which is essential in fields such as mathematics, science, and logic, where formal steps are necessary to validate findings or claims.

The other options do not carry the same implication of adhering to a formal procedure to attain an outcome. "Manipulate" suggests influencing or handling something in a skillful manner but lacks the formal aspect associated with proving. "Realise" refers to becoming aware of something or bringing something into existence, which does not imply a structured methodical process. "Modify" involves changing or adjusting something, but again, this does not reflect the formal steps necessary for proof. Therefore, "prove" is distinctly focused on the structured approach to validation, making it the appropriate selection.