Only 15^2 falls between 200 and 250.
15^2 = 225.
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Between 2,827 and 2,829
300
25 < 30 < 36 so that 52 < 30 < 62 196 < 200 < 225 so that 142 < 200 < 152 So the squares of the numbers 6, 7, ... 14 are the required numbers.
1,4,9,16,25,36,49,64,81,100,121,144,169,196.
There are 200.