Question

If $a<0,b>0,$ then $\sqrt{a}\cdot \sqrt{b}$ is equal to

• A. $-\sqrt{|a|\cdot b}$
• B. $\sqrt{|a|\cdot b}\cdot i$
• C. $\sqrt{|a|b}$
• D. None of the above

Answer 1

The correct option is B $\sqrt{|a|\cdot b}\cdot i$

$\sqrt{a}\sqrt{b}=\sqrt{a\cdot b}$ ($\because a<0$ and $b>0)$
$\because |a|=-a$,
Now,
$\sqrt{a\cdot b}=\sqrt{-|a|\cdot b}=\sqrt{|a|\cdot b}.i$