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

Efan Halliday 2021-09-21 Answered
Express \(\displaystyle{2}\sqrt{{{6}}}{\left({8}-{4}\sqrt{{{3}}}\right)}\) as a product in simplest form.

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Expert Answer

dieseisB
Answered 2021-09-22 Author has 12638 answers
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
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