Let, (a + ib)² = 0 - 8i

Now using, (a + b)² = a² + b² + 2ab

a² + (bi)² + 2abi = 0 - 8i

Since i² = -1

a² - b² + 2abi = 0 - 8i

Now, separating real and complex parts, we get

a² - b² = 0 …………..eq.1

2ab = -8…….. eq.2

a =

Now, using the value of a in eq.1, we get

– b² = 0

16 – b⁴ = 0

b⁴ = 16

Simplify and get the value of b², we get,

b² = -4 or b² = 4

As b is real no. so, b² = 4

b= 2 or b=

Therefore , a= -2 or a= 2

Hence the square root of the complex no. is -2 + 2i and 2 - 2i.