Why are there two answers???

[mentu960]

It all started in my pre-calc class when my teacher gave us a packet and he had us circle an answer to a question. I'm going to save you guys some time and just say that I came up with a situation in which he couldn't give me an answer. So I figured this would be my next best option, so I really encourage you all to help find out why there are two answers to this question...

http://www.facebook.com/home.php?#!/pho ... 136&ref=nf

the link leads to my facebook picture... it is to difficult to type out so that is the easiest way to view it... so if someone or a multitude of people can individually or collectively come up with a way to explain this problem that would be greatly appreciated.

[stapel_eliz]

Nothing displays. Sorry.

To learn how to type math, please read this article. Then please reply with a posting of your exercise here.

Thank you!

[mentu960]

sqrt(-3)^2 = sqrt(9) = 3

AND

sprt(-3)^2 = (sqrt(-3))^2 = (i (sqrt(3)))^2 = i^2 (sqrt(3)^2) = -1 (3) = -3

P.S. thank you for that article, I have been curious about the most efficient way to type mathematical terms for a long time B)

[stapel_eliz]

sqrt(-3)^2 = sqrt(9) = 3

If you mean , then you are taking the square root of 9. If, on the other hand, you mean , then you need to change to complex values:

. . . . .

As soon as you start dealing with negatives inside square roots (or any even-index root), you have to convert to complex numbers. You gain the ability to deal with negatives inside radicals; you lose the ability to switch around between powers and radicals (so you cannot move the squaring inside and outside and back again).