1000
One possible conjecture is that each square number up to 1000 has 4 factors. The conjecture is manifestly false, but it is still a conjecture.
1, 4, 25, 100, 1000
152 = 225 and 312 = 961 so there are 16 square numbers between 200 and 1000
02 + 02 = 0; all other numbers squared are greater than 0. Otherwise 25 (= 52) = 32 + 4262 + 82 = 100√100 = 10; √1000 ≈ 31.6, so largest square less than 1000 is 312Between 100 and 1000 there are 31-10 = 21 square numbers (22 if 100 itself is included since 100 = 102)
They are the squares of the numbers 1 to 31. Use a calculator to find them.
1000
One possible conjecture is that each square number up to 1000 has 4 factors. The conjecture is manifestly false, but it is still a conjecture.
1, 4, 25, 100, 1000
There are 31 perfect square numbers between 1 and 1000 (including 1).
152 = 225 and 312 = 961 so there are 16 square numbers between 200 and 1000
1001
A square number is any number multiplied by itself. 1 is a square number, since 1 x 1 = 1. 2 is not, since there is no integer that you can multiply by itself to get 2. 4 is the next square number, since 2 x 2 = 4. Squaring 3, 4, and 5 give the next three square numbers: 9, 16, and 25. To get the first thousand square numbers, take each of the first thousand natural numbers (1, 2, 3, ... 1000) and multiply them by themselves. This will produce the first thousand square numbers, ranging from 1 (1x1) to 1,000,000 (1,000 x 1,000).
There is an infinity of squares that are over 1000, starting with 322 = 1024.
1000+1000 1000x2
1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400 All the square numbers up to 20!
02 + 02 = 0; all other numbers squared are greater than 0. Otherwise 25 (= 52) = 32 + 4262 + 82 = 100√100 = 10; √1000 ≈ 31.6, so largest square less than 1000 is 312Between 100 and 1000 there are 31-10 = 21 square numbers (22 if 100 itself is included since 100 = 102)