√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.
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The squares of the numbers 32, 33, 34,...,44 the square of the first number 32 is 1024 the square of the last number 44 is 1936
There are six perfect squares which are factors of 2000.
sqrt(2000) = 44.7sqrt(20000) = 141.4So the perfect squares between 2000 and 20000 are the squares of 45 to 141 (inclusive)ie there are 97 perfect squares in the interval.
The question presumably refers to, 'How many squares of integers are between 1000 and 2000?' √1000 = 31.6 : √2000 = 44.7 The answer is the squares of the integers 32 to 44 . There are thus 13 squares of integers in the specified number range. 322 = 1024 : 332 = 1089 : 342 = 1156 : 352 = 1225 : 362 = 1296 : 372 = 1369 : 382 = 1444 : 392 = 1521 : 402 = 1600 : 412 = 1681 : 422 = 1764 : 432 = 1849 : 442 = 1936
3000