Eli5: What are real and non real roots?

Question

I keep googling it and I still don’t understand what they are and their differences 😭😭

In: 18

Answer 1

A root of a number X is finding the number that you have to multiply with itself to find X. The most common is the square root, where you have to multiply a number with itself once to find the target X. The square root of 4 is 2 (and -2) because 2×2=4. (You can of course have ‘higher’ roots.) The difference arises when you try to get a root of a target number X that is negative. Let’s say you want the square root of -4. Is it 2? No because 2×2 is not -4. Is it -2? No because -2x-2=4.
Damn.
The solution to this are non-real numbers, namely imaginary numbers, which is a very difficult topic I know nothing about and is out of the scope of ELI5.
This means that the square root of -4 is non real, i.e. a non-real root.