## sugarheart 2 years ago .

1. Mertsj

The deal is this....when you square an equation you sometimes end up with a "solution" that doesn't make the sentence true. Those are called extraneous roots. They are the reason your teacher tells you to always check the answers you get when solving radical equations. Sometimes they don't work. Let me show you an example.

2. Mertsj

|dw:1366677654241:dw|

3. precal

also, the domain helps in identifying extraneous solutions

4. Mertsj

And that answer will not check. It is an extraneous solution.

5. sugarheart

I got it, it's 5

6. Mertsj

7. sugarheart

Yes

8. Mertsj

Good for you!!!

9. Mertsj

Hey...just a minute. I don't think 5 will check.

10. Mertsj

|dw:1366677868347:dw|

11. Mertsj

12. sugarheart

What?

13. Mertsj

As you can see...5 does not make the sentence true.

14. Mertsj

So if 5 was accepted as a correct answer, someone has put the wrong answer into the computer program .

15. Mertsj

Didn't you also get -3 as an answer?

16. precal

you mean |dw:1366678251238:dw|

17. sugarheart

@precal Why does that matter though.. It wasn't my question it was his example

18. Mertsj

|dw:1366678291957:dw|

19. precal

because 13 is extraneous

20. Mertsj

You see...-3 is actually an answer. It checks. 5 is extraneous.

21. Mertsj

@precal That was an example I constructed to illustrate extraneous roots for the asker

22. precal

sorry Mertsj, saw your example and not the actual problem

23. Mertsj

np

24. precal

Key idea @sugarheart is that when solving solutions for square root equations or radicals, extraneous solutions do exist so we have to check for them

25. sugarheart

5 is the extraneous solution and that's why it's was the answer to my problem

26. Mertsj

oh. So they were asking for the extraneous root. Cool. Then it is right.

27. sugarheart

Yes lol

28. Mertsj

Yep. I reread the question. Always helps to know the question one is attempting to answer.

29. precal

extraneous solutions can also, occur in other functions (example logarithmic)