Question

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

• A. $-\sqrt{\mid a\mid b}$
• B. $\sqrt{\mid a\mid b}i$
• C. $\sqrt{\mid a\mid b}$
• D. None of these

Answer 1

Answer: (B)

$\sqrt{\mid a\mid b}i$

$\sqrt{a}.\sqrt{b}$
$=\sqrt{ab}$
However
$a<0$ and $b>0$
Hence
$-a>0$.
Thus
$\sqrt{ab}$ is imaginary.
Hence
$\sqrt{ab}$
$=\sqrt{-|a|b}$ since $a<0$ but $|a|>0$
$=\sqrt{i^2|a|b}$
$=i\sqrt{|a|.b}$