Question

Simplify the product: $\sqrt{6}(\sqrt{2}+\sqrt{3})$.

• A. $\sqrt{8}+3$
• B. $\sqrt{30}$
• C. $2\sqrt{3}+3\sqrt{2}$
• D. $4\sqrt{2}+3$

Answer 1

The correct option is C

$2\sqrt{3}+3\sqrt{2}$

Explanation for the correct option:

Given that $\sqrt{6}(\sqrt{2}+\sqrt{3})$
$$\begin{gathered} \Rightarrow \sqrt{6}(\sqrt{2}+\sqrt{3})=\sqrt{12}+\sqrt{18}\left[\because \sqrt{a}\times \sqrt{b}=\sqrt{a\times b}\right] \\ =\sqrt{2\times 2\times 3}+\sqrt{3\times 3\times 2} \\ =2\sqrt{3}+3\sqrt{2} \end{gathered}$$

Hence, option(C) is correct.