What is radical -1728 cubed?

Answer 1

The expression "radical -1728" refers to the square root of -1728, which is not a real number because you cannot take the square root of a negative number in the realm of real numbers. In the context of complex numbers, it can be expressed as ( \sqrt{-1728} = \sqrt{1728} i = 12\sqrt{12} i ). Cubing this value, ( (12\sqrt{12} i)^3 = 1728\sqrt{12^3} i^3 = -1728 \cdot 12\sqrt{12} = -20736\sqrt{12} ). Thus, the cube of the square root of -1728 is a complex number.