How many divisors of 3600 are perfect squares?

3600 = $2^4\times 3^2\times 5^2$. A divisor is a perfect square exactly when each exponent in it is even, so pick the power of 2 from {0, 2, 4}, of 3 from {0, 2} and of 5 from {0, 2}: $3\times 2\times 2=12$. (45 is the count of all divisors, $5\times 3\times 3.$)