Perfect squares..

$\large 15^2=225$ $\large 31^2=961$ The number of perfect squares would be $\large 31-15+1=17$

The first perfect square bigger than 200 is 15^2, and less than 1000 is 31^2. So there are (31 - 15) + 1 = 17 perfect squares.

There are following 17 perfect squares between 200 and 1000.

$225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, \text{and } 961.$

Here, $\left\lceil \sqrt { 200 } \right\rceil =15$ and $\left\lfloor \sqrt { 1000 } \right\rfloor =31$

So, from $15$ to $31$ we get $31-15+1=\boxed{17}$ number. It is the answer.