Mathematics

This is an interesting one........

For all real numbers x,

√(x)^2 = IxI = x if {x ≥ 0 and -x if x < 0}

So, √(-1)^2 = I-1I = -(-1) = 1

Now, many people assume that the result could be "-1" - due to following faulty "proof."

Step 1 √(-1)^2 =

Step 2 √(-1) * √(-1) =

Step 3 ( i * i ) =

Step 4 ( -1 )

The problem comes in the transition from Step 1 to Step 2.

In general, √(a * a) = √(a) * √(a) only if a ≥ 0. (Thus, we can't "split" the radicals in this manner.)

I think that's it !!!

while it's true that a*a = a ² for a<0

it's not true that sqrt(a ²) = a

for (a<0) sqrt(a ²) = -a

When working with real numbers the square root of a number is always 0 or greater.

I'm with Rom,
By convention, the square root of any number > 0 is positive.
Your question sqrt ([-1 ²])= sqrt (1) = +1

If the square root is in the question the answer is poitive. If you introduce the square root as a part of your working then the answer can be + or -

eg
If the question is y=sqrt(16)
then the answer is y=4

but
if the question is y ²=16
then you have to introduce the sqrt so the answer is y=+ or - sqrt(16) = +4 or -4