The square root of 3000 is 54.77 and the square root of 3200 is 56.57.
So the only perfect squares in the required number range are 552 = 3025 and 562 = 3126.
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√2000 ≅ 44.7 √3000 ≅ 54.8 The squares of 45 to 54 lie within the range 2000 to 3000. There are thus 10 perfect square numbers between 2000 and 3000.
1331 and 2197
If you include the number 3,000, there are exactly 2,001 4-digit numbers between 500 and 3000.
3000
All the numbers between 999 and 3000 are four-digit numbers. You need to subtract 3000 - 999 - 1. The extra -1 is to account for the fact that the numbers 999 and 3000, in this case, are not included.