There is an infinity of squares that are over 1000, starting with 322 = 1024.
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There are 31 perfect square numbers between 1 and 1000 (including 1).
The closest without going over 1000 is 961, which is the square of 31. The closest by going over 1000 is 1024, which is the square of 32.
They are the squares of the numbers 1 to 31. Use a calculator to find them.
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 are 24 perfect squares between 50 and 1000.