SOLUTION: This is probably a really stupid question. Please bear with me. I was reading this article https://www.mathsisfun.com/algebra/square-root.html It's helping me learn a lot. T

Question 1201162: This is probably a really stupid question. Please bear with me.

I was reading this article
https://www.mathsisfun.com/algebra/square-root.html
It's helping me learn a lot. The professor mentions the rule sqrt(xy) = sqrt(x)sqrt(y) then says "but only when x and y are both greater than or equal to 0"

But then there's this article
https://www.mathsisfun.com/numbers/imaginary-numbers.html
She or he breaks up the -9 into 9 x -1 and uses the square root rule only meant for positive numbers.
What gives? Why is the -1 allowed?

I don't understand sqrt(xy) = sqrt(x)sqrt(y) for x > 0 y > 0 but it clearly works(?) for negative numbers also.
I suppose I don't really understand imaginary numbers too much. I appreciate you reading this and helping me out.
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The statement from the professor in the first article you cite is incorrect -- or you misread the article.

(NOTE: I looked at the article. It seems poorly written and therefore confusing....)

The correct rule is that for all cases EXCEPT when x and y are BOTH negative.

the results are the same

the results are the same

But

the results are different -- because both numbers are negative

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