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Q: Which numbers are square numbers up to 1000?

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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 = 100âˆš100 = 10; âˆš1000 â‰ˆ 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)

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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

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 = 100âˆš100 = 10; âˆš1000 â‰ˆ 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)

There are 24 perfect squares between 50 and 1000.