Let, (a + ib)² = 5 + 12i

Now using, (a + b)² = a² + b² + 2ab

⇒ a² + (bi)² + 2abi = 5 + 12i

Since i² = -1

a² - b² + 2abi = 5 + 12i

now, separating real and complex parts, we get

a² - b² = 5…………..eq.1

2ab = 12……..eq.2

a =

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

– b² = 5

36 – b⁴ = 5b²

b⁴ + 5b² - 36= 0

Simplify and get the value of b², we get,

b² = -9 or b² = 4

As b is real no. so, b² = 4

b = 2 or b= -2

Therefore, a = 3 or a= -3

Hence the square root of the complex no. is 3 + 2i and -3 -2i.