How many prime numbers have squares between 100 and 300?
Since $10^2 =100$, $17^2 = 289$, and $18^2=324$, we know that the integers whose squares are between 100 and 300 are the integers between 10 and 18.  Between 10 and 18, 3 primes exist: 11, 13, 17, thus the answer is $\boxed{3}$.