Expert: Socrates - 8/9/2006

Question
I have just gotten to radical expressions in my algebra couse, and the book says that extraneous solutions were possible solutions you find in an equation, but when plugged back into the original equation, they don't work (like you end up taking the square of a negative number, or something.), and that made sense to me.

My teacher, though, said ALL negative answers to radical expressions are extraneous.  Like, finding the square of 1 provides only one real solution, 1.  And that -1 is extraneous.  But this doesn't make sense to me, because -1 times -1 gives one!

So I'm having problems understanding what makes an answer extraneous.  Please help!

Answer
An extraneous solution is one that doesn't satisfy the original radical equation. A negative number does not have to be extraneous. I don't know what your instructor meant by his/her statement. Maybe he meant that a solution that gives you a negative number under the square root sign is extraneous.

Anyway, here is a simple example with a negative number solution:

square root(x+18) = 4

you can square both sides and get x = -2 as the only solution. -2 is not extraneous, it satisfies the original radical equation. Perhaps you could show your instructor this example , either that or just ignore what your instructor said , we all make mistakes sometimes.