Why is the square root of -4 an imaginary number instead of -2?

Question

Why is the square root of -4 an imaginary number instead of -2?

In: Mathematics

Answer 1

Which number when multiplied to itself will give you -4?
We can simplify this even further. Remember that -4 is really (-1)*(4). So our aforementioned question now becomes a two part question.

(i) which number when multiplied to itself gives you 4? The answer is easy. It is 2.
(ii) which number when multiplied to itself gives -1? We can’t solve it. This is because when a negative number is multiplied to another negative number, you get a positive number as a result. Since we don’t have any answer but we need an answer, we give the answer a name. We call it the imaginary number. In short the ‘i’.

So now putting the answers from (i) and (ii) above, we get 2i as the square root of -4.