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There are 16 square numbers between 1 and 300: 2 to 17 inclusive. There is no square root of these numbers: only of their sum or product or average or some other operation.
The square root of 300 is irrational. Irrational numbers are infinitely dense and therefore the concept of consecutive numbers cannot be applied to irrational numbers.
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You can take the square root of a negative number by using complex numbers and the "i" operator. (-300)^.5 = (-1 * 300)^.5 = (-1)^.5 * 300^.5 = i17.32 because i = (-1)^.5