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This is true: the square root of a negative number is not a real number. The square root of a negative number is called a complex number (it's also referred to as an imaginary number)
On the GMAT, we are told to limit our mathematics to real number. So, for example, if we are told to solve x^2 = -4 for x, we know that x = root(-4) or x = -root(-4). Since root(-4) is not a rel number, we say (when taking the GMAT) that this equation has no solution.
As far as a list of Number Properties goes, the Official Guide explains everything you need to know.
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