We have the following expression:
[tex]3\sqrt[]{6}[/tex]
since
[tex]\sqrt[]{9}=3[/tex]
Our expression is equivalent to
[tex]\sqrt[]{9}\cdot\sqrt[]{6}[/tex]
Additionally, we can note that
[tex]\sqrt[]{6}=\sqrt[]{2\times3}=\sqrt[]{2}\cdot\sqrt[]{3}[/tex]
Then, we can write
[tex]\begin{gathered} \sqrt[]{9}\cdot\sqrt[]{6}=\sqrt[]{9}\cdot\sqrt[]{2}\cdot\sqrt[]{3} \\ \text{which is equivalent to} \\ \sqrt[]{9\cdot3}\cdot\sqrt[]{2}=\sqrt[]{27}\cdot\sqrt[]{2} \end{gathered}[/tex]
And finally, we can note that
[tex]\sqrt[]{27}\cdot\sqrt[]{2}=\sqrt[]{27\times2}=\sqrt[]{54}[/tex]
Therefore, the answers are:
[tex]\begin{gathered} \sqrt[]{9}\cdot\sqrt[]{6} \\ \\ \sqrt[]{27}\cdot\sqrt[]{2} \\ \\ \sqrt[]{54} \end{gathered}[/tex]
