The square root of a negative value is called an imaginary number.
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The square roots of any positive real number are a positive and a negative real number. The square roots of any negative real number are a positive and a negative imaginary number. The square roots of any imaginary number or any complex number are two complex numbers.
No, it is a complex number.
The negative square root of -144 is -12i - that is -12 times the square root of minus 1, ie √-144 = 12√-1. The above is a complex number, which I suspect is not the answer you wanted; there is no real number that is the square root of a negative number If you wanted the negative square root of 144, then it is -12.
Neither. (It is a complex number.)
They are called real numbers. Negative square roots must be complex numbers.