Final answer:
The state of Texas was an independent nation known as the Republic of Texas or the Lone Star Republic from 1836 to 1846 and is remembered on its flag with the word 'republic'.
Step-by-step explanation:
The U.S. state that was an independent nation for a short period is Texas, known as the Republic of Texas or the Lone Star Republic. This historical event took place between 1836 and 1846, when Texas declared itself independent from Mexico and functioned as a separate nation. After the Revolution ended in Texas, Sam Houston was elected as its first president. The Republic's independence, although lasting a decade rather than three weeks, is indeed celebrated with the inclusion of the word 'republic' on the state's flag. In 1846, the Republic of Texas was annexed to the United States, thus ending its status as an independent nation. This annexation process contributed to the start of the Mexican-American War, due to disputes over the boundary with Mexico.