Can you have a negative radical?

Answer 1

Well, no you cannot have a negative radical as asimplified and final answer, BUT you may begin with a negative radical and simplify it from there.

First lets say you have the radical: x= √-25

First, you need to know how to solve this. So, the way to go about solving this is to learn something called an imaginary unit i. i is defined as

i = √-1. This unit will allow you to turn a negative radical into a positive one, therefore allowing you to solve it from there.

So, now you can go back and solve the original problem:

x= √-25

x= √-1(√-25)

x= i√25

Then, because you now have a positive radical, you may now simplify it just as any other normal radical although you must include the i in the final answer.

x= i√25

x= i√5(5) or i√-5(-5)

x= ±5i

x= ±5i is the final and simplified answer. The plus or minus sign(±)is in front of 5i due to the fact that the radical was turned into a positive number. This means that either -5(-5)=25 or 5(5)=25. Therefore, you must use the plus or minus sign to indicate that it could be either.

By the way, i stands for imaginary.

And that is it! Please tell me if this information helped in some way and if you have any questions just ask!