Question

The value of $\sqrt{-3}\cdot \sqrt{-75}$ is

• A. $15$
• B. $15i$
• C. $-15$
• D. $-15i$

Answer 1

The correct option is C $-15$

$\sqrt{-3}=\sqrt{-1\times 3}=\sqrt{-1}\times \sqrt{3}=\sqrt{3}i$
And
$\sqrt{-75}=\sqrt{-1\times 75}=\sqrt{-1}\times \sqrt{75}=\sqrt{75}i$
$[\because \sqrt{-1}=i]$

Now,
$\sqrt{-3}\cdot \sqrt{-75}=\sqrt{3}i\times \sqrt{75}i=i^2\sqrt{3\times 75}=-\sqrt{225}[\because i^2=-1]=-15$