$\sqrt{(-1)^2}$: Is it -1 or 1?

[footmath]

Is it correct ?
$ \sqrt{(-1)^2} $ = $ \sqrt{(-1)}\sqrt{(-1)} $= $ i*i $=$ i^2 $ =$ -1 $
or
$ \sqrt{(-1)^2} $ = $ \sqrt{(1)} $=1

 

[eumyang]

You mean this?
$\text{1) }\sqrt{(-1)^2} = \sqrt{(-1)} \cdot \sqrt{(-1)} = i \cdot i = i^2 = -1$
$\text{2) }\sqrt{(-1)^2} = \sqrt{1} = 1$

Note that the product property of radicals,
$\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$
holds only if both a and b are non-negative.