What happens when I square root a negative number?

Answer 1

It depends on how advanced you are. At school level (unless specialising in pure mathematics) you will be told that the squares of both negative and positive numbers are positive. There are, therefore, no numbers that have a negative square and so the square root of negative number cannot exist.

Calculators, including those built into computers will confirm this by issuing an error message.

However, when you study advanced mathematics you learn about the complex field and discover that negative numbers do have square roots. they are linked to the imaginary square root of -1, which is denoted by i.

Thus for example, sqrt(-16) = sqrt(16)*i=4i

and sqrt(-10) = sqrt(10)*i etc.

In a way, this is like being told in infant school that you cannot take 5 away from 2. Later on, you learn that you can and the answer is a new kind of number: a negative number!