SOLUTION: determine if true, sometimes true or never true? a) if A is a real # then the square root of A represents a real # b) the conjugate of the square root of A + the square root

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Question 1142923: determine if true, sometimes true or never true?
a) if A is a real # then the square root of A represents a real #
b) the conjugate of the square root of A + the square root if B is found by replacing B with its opposite
c) if x<0 then the square root of X to the 2nd power = -x

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
(a)  sometimes.   (it is TRUE for non-negative real numbers and is FALSE for all negative real numbers)



(b)  sometimes.   (It is true for B= 0 and is FALSE for all other cases)



(c)  In the frame of the middle school Math curriculum, it is always true.


     In real Math (high school Math curriculum and the University/College Math level), the square root of a number 

     is NOT a NUMBER at all (!) : it is the set of two opposite numbers.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I will disagree slightly with tutor @ikleyn (as I have done in the past) regarding her answer for part c.

The meaning of "the square root of 9" does not change when you go from middle school to high school and beyond.

It will cause mathematical chaos if we can say that "the square root of 9 is a set of two different values". When we write a number like "square root of 9", it HAS TO have a single value.

If we are solving the equation sqrt%289%29%2Bx+=+10, we can't arbitrarily choose one of two different values for the square root of 9. THE square root of 9 is 3 (whatever level of math you are at); the number -3 is -sqrt%289%29%29.

"3 squared is 9": TRUE
"(-3) squared is 9": TRUE
"The number 9 has two square roots": TRUE
"THE square root of 9 is 3 or -3": FALSE
"THE square root of 9 is 3": TRUE

So the answer to part c is "TRUE".

Example: If x = -3, then x^2 = 9; THE square root of 9 is 3, which is -x.