The square root of $-64$ involves dealing with complex numbers since you are taking the square root of a negative number. In the realm of real numbers, there is no real square root for a negative number. However, in the realm of complex numbers, you can express the square root of $-64$ as:

$\sqrt{-64} = \sqrt{64} \times \sqrt{-1} = 8i$

where $i$ is the imaginary unit, defined by the property $i^2 = -1$. Therefore, the square root of $-64$ is $8i$.