\(\displaystyle\sqrt{{x}}{y}=\sqrt{{x}}\times\sqrt{{y}}\)

\(\displaystyle{4}\sqrt{{8}}\times\sqrt{{10}}={4}\sqrt{{{8}\times{10}}}\)

\(\displaystyle={4}\sqrt{{80}}\)

\(\displaystyle{80}={2}\times{40}\)

\(\displaystyle={2}\times{2}\times{40}\)

\(\displaystyle={2}\times{2}\times{2}\times{10}\)

\(\displaystyle={2}\times{2}\times{2}\times{2}\times{5}\)

\(\displaystyle={2}^{{4}}\times{5}\)

\(\displaystyle{4}\sqrt{{80}}={4}\sqrt{{{2}^{{4}}\times{5}}}\)

\(\displaystyle\sqrt{{{2}^{{4}}}}=\sqrt{{{\left({2}^{{2}}\right)}^{{2}}}}\)

\(\displaystyle={2}^{{2}}\)

=4

Thus,

\(\displaystyle{4}\sqrt{{80}}={4}\times{4}\times\sqrt{{5}}\)

\(\displaystyle={16}\sqrt{{5}}\)

\(\displaystyle{4}\sqrt{{8}}\times\sqrt{{10}}={4}\sqrt{{{8}\times{10}}}\)

\(\displaystyle={4}\sqrt{{80}}\)

\(\displaystyle{80}={2}\times{40}\)

\(\displaystyle={2}\times{2}\times{40}\)

\(\displaystyle={2}\times{2}\times{2}\times{10}\)

\(\displaystyle={2}\times{2}\times{2}\times{2}\times{5}\)

\(\displaystyle={2}^{{4}}\times{5}\)

\(\displaystyle{4}\sqrt{{80}}={4}\sqrt{{{2}^{{4}}\times{5}}}\)

\(\displaystyle\sqrt{{{2}^{{4}}}}=\sqrt{{{\left({2}^{{2}}\right)}^{{2}}}}\)

\(\displaystyle={2}^{{2}}\)

=4

Thus,

\(\displaystyle{4}\sqrt{{80}}={4}\times{4}\times\sqrt{{5}}\)

\(\displaystyle={16}\sqrt{{5}}\)