Final answer:
The Islamic community successfully took back Mecca in 630 AD after a series of battles, with the city surrendering to Muhammad's forces, leading to the conversion of its population to Islam and the cleansing of the Kaaba of idols.
Step-by-step explanation:
The Islamic community, under the leadership of Muhammad, took back Mecca in 630 AD. Between 625-630 CE, a series of battles occurred between Muhammad's growing Muslim community and the Meccans. Despite the internal conflicts within Medina, the community continued to gain support. In 630, Mecca surrendered to Muhammad's force without much resistance, and the population converted to Islam. Upon his return to Mecca, Muhammad cleansed the Kaaba of idols, reinstating monotheism and establishing the shrine as the focal point for Muslim worship and pilgrimage, thus confirming choice c. 630 AD as the correct answer.