Question

1. simplify the expression below.

\sqrt{18}\left(2 + \sqrt{6}\
ight) - 2\sqrt{3}

Explanation:

Step1: Simplify $\sqrt{18}$

$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$

Step2: Distribute $3\sqrt{2}$

$3\sqrt{2}(2+\sqrt{6}) = 3\sqrt{2} \times 2 + 3\sqrt{2} \times \sqrt{6}$
$= 6\sqrt{2} + 3\sqrt{12}$

Step3: Simplify $\sqrt{12}$

$3\sqrt{12} = 3\sqrt{4 \times 3} = 3 \times 2\sqrt{3} = 6\sqrt{3}$

Step4: Combine like terms

$6\sqrt{2} + 6\sqrt{3} - 2\sqrt{3} = 6\sqrt{2} + (6\sqrt{3}-2\sqrt{3})$
$= 6\sqrt{2} + 4\sqrt{3}$

Answer:

$6\sqrt{2} + 4\sqrt{3}$