Given: √-64
Principally, (±i)² = i² = -1, so √-1 = ±i, and in the same manner, if x>0, then √-x = ±(√x )·i.
But usually, conventional definitions are applied to evaluate the square roots of negative numbers:
√-1 = i, and √-x = (√x )·i, x>0. Thus, √-64 is evaluated as shown below:
√-64 = √-1·√64 = √-1·√8² =8i
CK: (8i)² = 64·i² = -64 CKD.
Therefore, the answer is: √-64 = 8i