Question

Find the value of $\sqrt{2}\sqrt{-3}$:

• A. $\sqrt{6}$
• B. $-\sqrt{6}$
• C. $\mathrm{i}\sqrt{6}$
• D. None of these

Answer 1

The correct option is C

$\mathrm{i}\sqrt{6}$

Explanation for correct option

Calculating the value of the given expression:

Given expression is: $\sqrt{2}\sqrt{-3}$

On solving we get:

$$\begin{gathered} =\sqrt{2}\sqrt{-3} \\ =\sqrt{2}\sqrt{3}\sqrt{-1}\left[\because \sqrt{\mathrm{ab}}=\sqrt{\mathrm{a}}\sqrt{\mathrm{b}}\right] \\ =\sqrt{2}\sqrt{3}\mathfrak{i}\left[\because \sqrt{-1}=\mathfrak{i}\right] \\ =\sqrt{6}\mathfrak{i}\left[\because \sqrt{a}\sqrt{b}=\sqrt{ab}\right] \end{gathered}$$

Hence, the correct answer is Option (C).