Let, (a + ib)² = 16 -30i

Now using, (a + b)² = a² + b² + 2ab

a² + (bi)² + 2abi = 16 - 30i

Since i² = -1

a² - b² + 2abi = 16 - 30i

Now, separating real and complex parts, we get

a² - b² = 16…………..eq.1

2ab = -30…….. eq.2

a =

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

– b² = 16

– b⁴ = 16b²

b⁴ +16b² - 225= 0

Simplify and get the value of b² , we get,

b² = -25 or b² = 9

as b is real no. so, b² = 9

b= 3 or b= -3

Therefore , a= -5 or a= 5

Hence the square root of the complex no. is -5 + 3i and 5 - 3i.