Question

Simplify the following expression $\left(3+\sqrt{3}\right)\left(2+\sqrt{2}\right)$

Answer 1

Given that: $\left(3+\sqrt{3}\right)\left(2+\sqrt{2}\right)$

On opening and solving the brackets, we get

$$\begin{gathered} \left(3+\sqrt{3}\right)\left(2+\sqrt{2}\right) \\ =3\times 2+3\sqrt{2}+2\sqrt{3}+\sqrt{3}\sqrt{2} \\ =6+3\sqrt{2}+2\sqrt{3}+\sqrt{6} \end{gathered}$$

Hence, $\left(3+\sqrt{3}\right)\left(2+\sqrt{2}\right)$ is $6+3\sqrt{2}+2\sqrt{3}+\sqrt{6}$