Answer
a and b must be non-negative if $\sqrt a . \sqrt b$ = $\sqrt ab$
Let us consider that a and b are negative:
then,
$\sqrt -a . \sqrt -b$ = -$\sqrt ab$ $\ne$ $\sqrt ab$
Work Step by Step
a and b must be non negative if $\sqrt a . \sqrt b$ = $\sqrt ab$
To prove this let us consider that a and b are negative.
$\sqrt -a$ = $(\sqrt a) $ $\times$ i
where i = $\sqrt -1$ which is imaginary
same for b
$\sqrt -b$ = $(\sqrt b) $ $\times$ i
$\sqrt -a . \sqrt -b$ = $(\sqrt a) $ $\times$ i $\times $$(\sqrt b) $ $\times$ i
= $(\sqrt a) $ $\times $$(\sqrt b) $ $\times$$ i^{2} $
as $ i^{2} $ = -1 then
$(\sqrt a) $ $\times $$(\sqrt b) $ $\times$$ i^{2} $
= -$(\sqrt a) $ $\times $$(\sqrt b) $
= -$\sqrt ab$ $\ne$ $\sqrt ab$
so a and b cannot be negative, they must be non-negative
