Let, (a + ib)² = -15 - 8i

Now using, (a + b)² = a² + b² + 2ab

a² + (bi)² + 2abi = -15 -8i

Since i² = -1

a² - b² + 2abi = -15 - 8i

Now, separating real and complex parts, we get

a² - b² = -15…………..eq.1

2ab = -8…….. eq.2

a =

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

– b² = -15

16 – b⁴ = -15b²

b⁴ - 15b² - 16= 0

Simplify and get the value of b² , we get,

b² = 16 or b² = -1

As b is real no. so, b² = 16

b= 4 or b= -4

Therefore , a= -1 or a= 1

Hence the square root of the complex no. is -1 + 4i and 1 - 4i.