4. Among the 1001 radicals $\sqrt{1008}, \sqrt{1009}, \cdots, \sqrt{2008}$, the number of radicals that are of the same type as the quadratic radical $\sqrt{2016}$ is ( ) .
(A) 3
(B) 4
(C) 5
(D) 6
4. A.

Notice that
$$
\sqrt{2016}=\sqrt{2^{5} \times 3^{2} \times 7}=12 \sqrt{14} \text {. }
$$

Let the similar radical be $m \sqrt{14}$ (where $m$ is a positive integer). Then $\sqrt{1008} \leqslant m \sqrt{14} \leqslant \sqrt{2008}$, which means $\sqrt{72} \leqslant m \leqslant \sqrt{143 \frac{3}{7}}$.

And $8<\sqrt{72}<9,11<\sqrt{143 \frac{3}{7}}<12$, therefore, the value of $m$ is $9,10,11$.