Final answer:
To keep the Xiongnu from invading, Chao Cuo likely would have recommended a combination of military settlements on the border, influencing nearby tribes as buffers, hiring skilled professional soldiers, and a mixture of diplomatic tributes and cultural assimilation tactics.
Step-by-step explanation:
Chao Cuo's recommendations to prevent the Xiongnu from invading China included a combination of military strategies and diplomatic efforts. His approach seemed to favor using Chinese influence over nearby tribes and territories as a bulwark against the Xiongnu. Tactics included establishing military colonies along the frontiers, employing tribal chieftains as vassals to protect the border and to stir conflict amongst the Xiongnu, and selectively hiring professionals from border areas as soldiers rather than relying on a universal male draft. Additionally, there were periodic attempts to assimilate or control various factions of the Xiongnu, by providing tributes or by forcing them to submit to Chinese authority and receive Chinese cultural influences, such as educating a hostage prince from the aristocracy.
These efforts were part of a broader context of Han-Xiongnu relations where sometimes the Xiongnu and the Chinese mutually benefited from trade, and other times the Xiongnu leveraged their military strength to exact tributes from China. The Han dynasty employed various strategies ultimately aiming to outflank the Xiongnu, minimize their threats, and contain their influence.