-1 is equal to +1

We all know,     a = √a * √a = √(a*a)

Which implies,     -1 = √(-1) * √(-1) = √{(-1)(-1)} = √1 = 1

Of course, it can't be true.

Then what could be wrong?

We define,     a = √a * √a     or,     √ab = √a * √b

But it is valid only when at least one of     a & b     is non-negative.