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No, but it is irrational, because there is no rational number whose square is two. Imaginary numbers are the square roots of negative numbers.
If the square root is a whole number, then the square of the square root, the original number, is also a whole number; all whole numbers can be expressed as themselves over 1, and so are rational numbers. The answer is thus any square number, ie the square of the natural numbers: 1 (1²), 4 (2²), 9 (3²), 16 (4²), etc.
The nearest number whose square ≤ 10000 is 100. Then the greatest odd number less that 100 is 99 so there are 50 odd numbers in the range 1- 99 inclusive whose squares are less than 10000.
There are an infinite number of square numbers and prime numbers whose sums are a prime number. Examples are 202 + 103 = 503, 22 + 13 = 17, 102 + 601 = 701, 22 + 163 = 167, 42 + 141 = 157, etc.
A perfect square number is a number, whose square root is an integer. Examples are 1, 4, 9, 16, 25, .... The square roots of these numbers are {1,2,3,4,5,...} and {-1,-2,-3,-4,-5,...}