What is the 1000th number that isn't a perfect square?

Answer 1

To find the 1000th number that isn't a perfect square, we first recognize that the perfect squares up to ( n ) are given by the integers ( 1^2, 2^2, 3^2, \ldots, k^2 ) where ( k^2 \leq n ). The number of perfect squares up to ( n ) is ( \lfloor \sqrt{n} \rfloor ). Therefore, the count of non-perfect square numbers up to ( n ) is ( n - \lfloor \sqrt{n} \rfloor ). Solving the equation ( n - \lfloor \sqrt{n} \rfloor = 1000 ) gives ( n \approx 1000 + 31 = 1031 ). Thus, the 1000th number that isn't a perfect square is 1031.