\(\displaystyle{11}\cdot\sqrt{{48}}={11}\sqrt{{{16}\cdot{3}}}\) Rewrite 48 as a product.

\(\displaystyle={11}\cdot\sqrt{{16}}\cdot\sqrt{{3}}\) Use the rule \(\displaystyle\sqrt{{x}}{y}=\sqrt{{x}}\cdot\sqrt{{y}}\)

\(\displaystyle={11}\cdot{4}\cdot\sqrt{{3}}\) Evaluate sqrt16=4

\(\displaystyle={44}\sqrt{{3}}\) Multiply

\(\displaystyle={11}\cdot\sqrt{{16}}\cdot\sqrt{{3}}\) Use the rule \(\displaystyle\sqrt{{x}}{y}=\sqrt{{x}}\cdot\sqrt{{y}}\)

\(\displaystyle={11}\cdot{4}\cdot\sqrt{{3}}\) Evaluate sqrt16=4

\(\displaystyle={44}\sqrt{{3}}\) Multiply