Why all "Communist" countries call themselves a "Republic", and why after my Communism-trip I couldn't become a Socialist

Teacher: "What's the square root of 144?"; Actually, in theory every "Communist" country is still in its Socialist phase officially called "The Dictatorship Of The Proletariat"/workers. When Socialism has turned society on its head and money is rendered obsolete, the Government is supposed to dismantle itself and local governments are meant to become highest authority; Teacher; ...Math sucks