WILL MEDAL AND FAN! Which of the following are true about solving radical equations algebraically? (listed below b/c I couldn't fit it all in this first box)

Question

hhopke · Answer

-Isolate the radical part of the equation on one side and anything else on the other
-Raise both sides of the equation to a power that will undo the radical (2 for a square root, 3 for a cube root, etc.)
-If you check your answer by graphing both sides of the radical equation and your graphs don't cross, there is no intersection and no solution to the equation
-If there are radicals on both sides of the equation, the problem must be solved graphically
-When squaring both sides, it is possible that the equation will turn into a quadratic and will have two possible answers
-Sometimes you will have radicals on both sides; that is okay

hhopke · Answer

you there, @Directrix?

directrix · Answer

Yes. I'm here thinking about this problem.

directrix · Answer

Have you found any statements yet that you think are true?

hhopke · Answer

Well, I know that the second one (raising powers) is true b/c we did it in class today, and...

hhopke · Answer

I'm pretty sure the first one (Isolation) is right but I'm not positive.

hhopke · Answer

I know that the third one (checking answers) is right, but the question asks for truths about solving algebraically (the online thing is picky- it's like one of those weird riddles).

directrix · Answer

I agree with these two so far:

-Isolate the radical part of the equation on one side and anything else on the other

 -Raise both sides of the equation to a power that will undo the radical (2 for a square root, 3 for a cube root, etc.)

hhopke · Answer

And I'm not sure about the last three.

directrix · Answer

This is true. I just read a discussion about this on a website. I had never thought of checking solution this way.  

Add this to the true list:

-If you check your answer by graphing both sides of the radical equation and your graphs don't cross, there is no intersection and no solution to the equation

directrix · Answer

This has to be false:

-If there are radicals on both sides of the equation, the problem must be solved graphically

That type radical equation can be done algebraically.

directrix · Answer

This seems true to me:

-When squaring both sides, it is possible that the equation will turn into a quadratic and will have two possible answers

Try squaring both sides of this:

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