What is wrong with this logic?

Question

(-1)(-1)=1
sqrt[(-1)(-1)]=sqrt[1]
sqrt[(-1)]sqrt[(-1)]= sqrt[1]
so
i x i =-1 =1

Answer 1

What's wrong with it is that every number has two square roots. The validity of the manipulation √(xy) →√x√y is derived from the equality (xy)² = x²y². However, this equality also holds for (-xy)², so all you can really say about √x√y is that it is equal to ±√(xy). Thus, all you have managed to prove is that -1=±1, which is true, since -1=-1.

Answer 2

Firstly please consider that in the 3rd line, sqrt[1] has two solutions, +/-1.
The logic is wrong in the third line going into the forth line.

sqrt[(-1)]sqrt[(-1)] = sqrt[1]

--> i x i = sqrt[1]
{squaring both sides in order to remove the sqrt}

i^2 x i^2 = 1.

Therefore that logic is incorrect

Answer 3

sqrt (1)=+/- 1

Answer 4

sqrt[(-1)(-1)] can't b split into sqrt[(-1)]sqrt[(-1)] .........
as if done the answer will be + or - (i x i)

Answer 5

Hard to understand

Answer 6

sq rt of -1 is indeterminate and so
sq.rt(-1)*sq.rt(-1) is not equal to sq.rt(1)

Answer 7

what is " i " ?

if i is a constant, (i x i) can never be -1...
because...
no matter i is a positive or negative constant, the answer will ALWAYS be a posititve value...

is it what you expected for the explaination?