The square root of a negative number is imaginary, but the square root of -1 is given the symbol i and this forms the basis of complex numbers (effectively 2-dimensional numbers) which have a real part and an imaginary part. So, to represent the square root of a negative number you negate it to make it positive, evaluate the square root and then make this result a multiple of i.
√-1=i; √-5=i√5; √-4=2i; √-3=i√3.
Because there are two square roots in each case, √-1=±i, etc., because i2=(-i)2=-1.