How many positive integers less than 100 are both a square and a cube?
To be both a square and a cube, a number must be a perfect sixth power, since a square is a second power and a cube is a third power. The only perfect sixth powers less than 100 are 1 and 64, since 2^6 = 64 and 3^6 = 729, which is too big. Therefore, there are only two such numbers: 1 and 64. 