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Carson Wolfe
Sep 15, 2019

Square Root vs 1/2 Power

in Math Problems

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?

4 comments
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Louis Romao
Sep 15, 2019

-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.

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Ian Fowler
Sep 15, 2019  ·  Edited: Sep 15, 2019

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.

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Louis Romao
Sep 15, 2019  ·  Edited: Sep 15, 2019

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).


0
Ian Fowler
Oct 18, 2019

@Louis Romao

This is, of course, perfectly correct. To the original poster - always remember 3x^2 is not the same as (3x)^2

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4 comments