sqrt(2000) = 44.7
sqrt(20000) = 141.4
So the perfect squares between 2000 and 20000 are the squares of 45 to 141 (inclusive)
ie there are 97 perfect squares in the interval.
√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.
There are six perfect squares which are factors of 2000.
20000
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
10
√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.
There are six perfect squares which are factors of 2000.
20000
The perfect cubes between 1000 and 2000 are 1000 (10³) and 1331 (11³). Among these, 1000 is the only even perfect cube. Therefore, the only perfect cube that is an even number between 1000 and 2000 is 1000.
20000 + 2000 + 900 + 80 + 7 = 22987
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
20000
1000000 divided by 50 = 20000
20000
10
2000
2000