Find the square roots of 2 + isqrt(5)

Since we’re finding the square roots of 2 + isqrt(5) then (x+iy)^2 = 2 + isqrt(5)Thereforex^2 + 2ixy - y^2 = 2 + isqrt(5)Take real and imaginary parts it followsx^2 - y^2 = 2 and 2ixy = isqrt(5)solving this simultaneous equation for x and yx = +- sqrt(10)/2 and y = +- sqrt(2)/2So, answering the question, the square roots of 2 + isqrt(5) are+- sqrt(10)/2 +- isqrt(2)/2