The positive integers whose squares are less than 1000 are:
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
202 = 400
212 = 441
222 = 484
232 = 529
242 = 576
252 = 625
262 = 676
272 = 729
282 = 784
292 = 841
302 = 900
312 = 961
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square numbers 1 to 1000
1000
1, 4, 25, 100, 1000
152 = 225 and 312 = 961 so there are 16 square numbers between 200 and 1000
There are 5 square numbers under 30: 1, 4, 9, 16, and 25.