complex numbers - Can square roots be negative?

1955 AHMSE Problem 20 asks when $\sqrt{25 - t^2} + 5 =0.$

I know square root of real numbers cannot be negative. So t cannot be real.

But I don't know whether imaginary numbers' square root can be negative or not. I think square roots can never be negative. Also, I don't think we can classify imaginary numbers as positive or negative.

Can square roots of imaginary numbers be negative?