Negative number DO NOT have square roots.
We have to move into the realms of IMAGINARY numbers.
sqrt(-3) = sqrt(-1 X 3)
sqrt(-1) X sqrt(3)
The square root of '-1' has NOT been solved, and is given the symbol 'i'. Small case 'i'
The sqrt(3) = 1.732050808.... Is an irrational number.
NB THe square roots of prime numbers, '3' being a Prime number, are irrational.
Hence sqrt(-3) = 1.732....i is the 'at best' answer!!!!!
NB If you can solve the Square Root of '-1', then the mathematical/scientific world wants to know!!!!!