Why is it when I take
-1^(1/2) I get -1,
but when I take
sqrt(-1) I get undefined (or i in the imaginary world)?
Aren't taking a number to the 1/2 power and taking the square root of that number the same?
I would like to know if there is any method to make an estimation on how big it is a number, in terms of orders of magnitude of n! when n is a big number.
-1^(1/2) is not equal to sqrt(-1).
When evaluating -1^(1/2), the exponent is only being applied to the 1 and the negative is added later.
When evaluating sqrt(-1), the square root is being applied to -1.
(-1)^(1/2) = sqrt(-1) is a true statement.
I have read Loius' response, but before I comment further, it would be very helpful to know more details about the reasoning you used to get -1^(1/2) equal to -1. After that, I think I can help you sort out why -1 is incorrect. "
"Aren't taking a number to the 1/2 power and taking the square root of that number the same? " is true but I am not sure how that lead you to -1. Thanks.
The problem is not in the exponent, rather the base.
-1^(1/2)=-sqrt(1)=-(1^(1/2))=-1
sqrt(-1)=(-1)^(1/2)=i
Notice the difference in the base.
Also recall order of operations: Exponents are evaluated before multiplying by the negative (ie. -1).
@Louis Romao
This is, of course, perfectly correct. To the original poster - always remember 3x^2 is not the same as (3x)^2