# Express 2\sqrt{6}(8-4\sqrt{3}) as a product in simplest form.

Express $$\displaystyle{2}\sqrt{{{6}}}{\left({8}-{4}\sqrt{{{3}}}\right)}$$ as a product in simplest form.

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dieseisB
Given:
$$\displaystyle{2}\sqrt{{{6}}}{\left({8}-{4}\sqrt{{{3}}}\right)}$$
open the bracket then multiply
$$\displaystyle={2}\times{8}\sqrt{{{6}}}-{2}\times{4}\sqrt{{{6}}}\times\sqrt{{{3}}}$$
$$\displaystyle={16}\sqrt{{{6}}}-{8}\sqrt{{{6}\times{3}}}$$
$$\displaystyle={16}\sqrt{{{6}}}-{8}\sqrt{{{3}\times{3}\times{2}}}$$
square root of $$\displaystyle{3}\times{3}$$ is 3 therefore
$$\displaystyle={16}\sqrt{{{6}}}-{3}\times{8}\sqrt{{{2}}}$$
$$\displaystyle={16}\sqrt{{{6}}}-{24}\sqrt{{{2}}}$$ - Answer