[tex]4\sqrt[]{3}\times2\sqrt[]{27}[/tex]
To multiply the above numbers, here are the steps:
1. Multiply the whole number and the radicands.
[tex]\begin{gathered} 4\times2=8 \\ \sqrt[]{3}\times\sqrt[]{27}=\sqrt[]{81} \end{gathered}[/tex]
2. Get the square root of 81.
[tex]\sqrt[]{81}=9[/tex]
3. Multiply the answer in #2 to the product of the whole numbers.
[tex]8\times9=72[/tex]
Therefore, the product of 4√3 and 2√27 is 72.
The result is rational because it can be written as the ratio of two integers and its decimal expansion does terminate or repeat.
