Find the following products and express answers in simplest radical form. All va

Caelan 2021-09-16 Answered
Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers.
\(\displaystyle{\left({3}\sqrt{{{2}}}-{5}\sqrt{{{3}}}\right)}{\left({6}\sqrt{{{2}}}-{7}\sqrt{{{3}}}\right)}\)

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Expert Answer

komunidadO
Answered 2021-09-17 Author has 20987 answers
Give that,
\(\displaystyle{\left({3}\sqrt{{{2}}}-{5}\sqrt{{{3}}}\right)}{\left({6}\sqrt{{{2}}}-{7}\sqrt{{{3}}}\right)}\)
Consider,
\(\displaystyle{\left({3}\sqrt{{{2}}}-{5}\sqrt{{{3}}}\right)}{\left({6}\sqrt{{{2}}}-{7}\sqrt{{{3}}}\right)}={3}\sqrt{{{2}}}{\left({6}\sqrt{{{2}}}-{7}\sqrt{{{3}}}\right)}-{5}\sqrt{{{3}}}{\left({6}\sqrt{{{2}}}-{7}\sqrt{{{3}}}\right)}\)
\(\displaystyle={3}\sqrt{{{2}}}{\left({6}\sqrt{{{2}}}\right)}-{3}\sqrt{{{2}}}{\left({7}\sqrt{{{3}}}\right)}-{5}\sqrt{{{3}}}{\left({6}\sqrt{{{2}}}\right)}+{5}\sqrt{{{3}}}{\left({7}\sqrt{{{3}}}\right)}\)
\(\displaystyle={18}\times{2}-{21}\sqrt{{{6}}}-{30}\sqrt{{{6}}}+{35}\times{3}\)
\(\displaystyle={36}+{105}-\sqrt{{{6}}}{\left({21}+{30}\right)}\)
\(\displaystyle={141}-{51}\sqrt{{{6}}}\)
Answer: \(\displaystyle{\left({3}\sqrt{{{2}}}-{5}\sqrt{{{3}}}\right)}{\left({6}\sqrt{{{2}}}-{7}\sqrt{{{3}}}\right)}={141}-{51}\sqrt{{{6}}}\)
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