Question

Solve the radicals √-64

Answer 1

√-64 is undefined

Answer 2

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 

Answer 3

This is the same as 8sqrt(-1)=8i (imaginary number).