I don't understand why this problem is considered unsolvable: (-4)^1/2

Question

accessdenied · Answer

What were you considering for a solution?

anonymous · Answer

It says the answer is suppose to be unsolvable but I don't know why

accessdenied · Answer

Were you considering that (-4)^(1/2) is the same as the square root of -4 ?
   $ (-4)^{1/2} = \sqrt{-4} $

anonymous · Answer

Um, idk, I guess yes I was. I'm teaching this stuff to myself and the text didn't explain

anonymous · Answer

So, because its not a sq. root but rather a simple negative number...

accessdenied · Answer

You said you don't know why this is unsolvable.  So I was wondering if you had an idea for how it might be solved, so we can go over why it might not work!

accessdenied · Answer

Let's call our expression, y.
   y = (-4)^(1/2)
Now we can square both sides.
   y^2 = - 4
So, think about what you could put in for y whose square is negative four.

If we put in a positive number, its square is also a positive number.  2^2 = +4.
If we put in a negative number, it is ALSO a positive number because we multiply -2 by -2.  The negatives cancel!  (-2)^2 = (-2)(-2) = 4.

This is where real number solutions do not exist.  However, if you go further you might learn about complex numbers, whose basis is the "number" i = sqrt(-1).  But in our case, unsolvable means "not a real number".