Solution of square root of the square of (-1)

Asked Feb 10 '20 at 18:48

Active Feb 10 '20 at 19:06

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What is the result of $$ \sqrt{(-1)^2} ?$$ I see two potential ways of solving this. First, by direct calculation $$ \sqrt{(-1)^2} = \sqrt{1} = 1. $$ Second, by applying the power rule $$ \sqrt{(-1)^2} = (-1)^{2^{1/2}} = (-1)^{2/2} = -1. $$

Intuitively, I would say the first approach is correct. However, I did not find any restrictions to the power rule that would rule out the second solution.

edited Feb 10 '20 at 19:06

asked Feb 10 '20 at 18:48

Schorsch

3

Normal exponent rules don't apply to negative bases. So the first approach is correct. – Dave Feb 10 '20 at 18:51
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Welcome to Mathematics Stack Exchange. Cf. this question – J. W. Tanner Feb 10 '20 at 18:55
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Take a look at this question https://math.stackexchange.com/questions/3345202/square-root-of-a-product-of-negative-numbers – sam wolfe Feb 10 '20 at 19:08
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Does this answer your question? Square root of a product of negative numbers – sam wolfe Feb 10 '20 at 19:08
Thank you for your answers! My question is answered thoroughly in the thread proposed by @J.W.Tanner . – Schorsch Feb 10 '20 at 19:09
I think you meant $2 \cdot 1/2$, not $2^{1/2}$. – Hew Wolff Feb 10 '20 at 19:28

Solution of square root of the square of (-1)

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