jmc

To begin, take out the factor of 10 and look at 3267. With a quick check, we can see this number is divisible by 3. Taking out factors of 3, we find $3267=3\cdot 1089=3^2\cdot 363=3^3\cdot 121$. Since $121=11^2$, the complete factorization is $32670=10\cdot 3^3\cdot 11^2$. Therefore, $\sqrt{32670}=\boxed{33\sqrt{30}}$.