Question

To find the equation 4\sqrt{8}\times\sqrt{10}=?

Irrational numbers
ANSWERED
asked 2021-01-31

To find the equation \(4\sqrt{8}\times\sqrt{10}=?\)

Answers (1)

2021-02-01
\(\displaystyle\sqrt{{x}}{y}=\sqrt{{x}}\times\sqrt{{y}}\)
\(\displaystyle{4}\sqrt{{8}}\times\sqrt{{10}}={4}\sqrt{{{8}\times{10}}}\)
\(\displaystyle={4}\sqrt{{80}}\)
\(\displaystyle{80}={2}\times{40}\)
\(\displaystyle={2}\times{2}\times{40}\)
\(\displaystyle={2}\times{2}\times{2}\times{10}\)
\(\displaystyle={2}\times{2}\times{2}\times{2}\times{5}\)
\(\displaystyle={2}^{{4}}\times{5}\)
\(\displaystyle{4}\sqrt{{80}}={4}\sqrt{{{2}^{{4}}\times{5}}}\)
\(\displaystyle\sqrt{{{2}^{{4}}}}=\sqrt{{{\left({2}^{{2}}\right)}^{{2}}}}\)
\(\displaystyle={2}^{{2}}\)
=4
Thus,
\(\displaystyle{4}\sqrt{{80}}={4}\times{4}\times\sqrt{{5}}\)
\(\displaystyle={16}\sqrt{{5}}\)
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