Let, (a + ib)² = 7 - 30i

Now using, (a + b)² = a² + b² + 2ab

a² + (bi)² + 2abi = 7 - 30i

Since i² = -1

a² - b² + 2abi = 7 - 30i

Now, separating real and complex parts, we get

a² - b² = 7 …………..eq.1

2ab =30…….. eq.2

a =

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

– b² = 7

450 – b⁴ = 7b²

b⁴+ 7b² - 450= 0

Simplify and get the value of b² , we get,

b² = -25 or b² = 18

As b is real no. so, b² = 18

b= or b=

Therefore , a= 5 or a= - 5

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