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

1 Answer
Jul 16, 2015

Answer:

#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).