Question

How do you simplify: the square root of -125?

Answer 1

`5i*sqrt(5)`

Explanation:

Let's break this into it's factors:

`sqrt(-125)=sqrt(-1*5*5*5)=sqrt(-1)*sqrt(5)*sqrt(5^2)`

We can evaluate the first and 3rd terms here to give:
`sqrt(-1)*sqrt(5)*sqrt(5^2)=5i*sqrt(5)`

Where `i=sqrt(-1)` (a concept from complex analysis).