What happens if I get a negative square or cube root?
Answer
If you end up having a negative for your square root. You simply replace the negative with an i. Since a negative square root is declared not a real number. Also any real number multiplied by itself should always result in a positive number. However, in this case since it is negative it has to be expressed using an (i) which stands for an imaginary number which defines as the square root of -1.
Now here are some examples
1. Lets say we have the square root of negative 25
Remember negative square roots are replace by I and since the square root of 25 is 5. Our solution is 5i.
2. Here we have the cube root of negative 8.
We know that the cube root of 8 is 2 and since it is negative we have to use an i. Therefore, our solution is 2i
3. Say we are given the square root of -125.
Now since 125 is not a perfect square we can break it down to where by factoring. We can break down 125 by 25 times 5. Once we do that we can see that 25 is a perfect square which is 5. Therefore, our answer is 5i with the square root of 5.