complex numbers - Is product of two square roots of two integers square root of their products?

Suppose
$a,b\in \mathbb{Z}$.
Is it true
$\sqrt{a}\sqrt{b}=\sqrt{ab}$.
If so, then $\sqrt{-1}\sqrt{-1}=\sqrt{(-1)(-1)}=\sqrt{1}=1$

But we know $\sqrt{-1}=i$ and so $i^2=-1.$
Finally we get $i^2=-1=1.$
Which is not true.
What is the logic behind it?

Thank you in advance.