What is the value of square root of -4?

Answer 1

Original Answer: 2


This is actually incorrect, 2 is the square root of 4 not -4 since it does not take into account the presence of the negative.


In order to find the square root (sqrt) of -4 we need to consider two facts:


(1) -N = N x -1 , where N is any number.


(2) sqrt (X x Y) = sqrt (X) x sqrt (Y)


This gives sqrt (-N) = sqrt (N x -1) = sqrt (N) x sqrt (-1)


It is generally accepted that the square root of (-1) is represented by the imaginary number i . (For more on i see http://en.wikipedia.org/wiki/Imaginary_number)

Substituting 4 for N we get sqrt (-4) = sqrt (4) x i = 2i