Let, (a + ib)² = -7 + 24i

Now using, (a + b)² = a² + b² + 2ab

a² + (bi)² + 2abi = -7 + 24i

Since i² = -1

a² - b² + 2abi = -7 + 24i

Now, separating real and complex parts, we get

a² - b² = -7…………..eq.1

2ab = 24…….. eq.2

a =

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

– b² = -7

144 – b⁴ = -7b²

⁴ - 7b² - 144= 0

Simplify and get the value of b² , we get,

b² = -9 or b² = 16

As b is real no. so, b² = 16

b= 4 or b= -4

Therefore, a= 3 or a= -3

Hence the square root of the complex no. is 3 + 4i and -3 -4i.