How many republics made up the USSR?

Depends what you mean by a 'republic.' If you mean, 'how many countries became independent when the USSR broke up' the answer is 15. If you mean, 'how many sub-Soviet government organisations were there,' well, the answer varies a bit. Under Khrushchev, for example, the number was 105. Under Brezhnev, some merged so it went down to about 98 at one point. Most of these were part of what is now the Russian Federation. If you go for 'around 100' nobody's going to query it.