The expression to simplify is:
![9\sqrt[]{2}(4\sqrt[]{6})](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/f28usxpr1xnw48uxrz16.png)
When we are multiplying two racial expressions, we multiply the constants together and the square roots together. So, the next step is:
![\begin{gathered} 9\sqrt[]{2}(4\sqrt[]{6}) \\ =(9*4)(\sqrt[]{2}*\sqrt[]{6}) \\ =36(\sqrt[]{2}*\sqrt[]{6}) \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/20o2v28jm7j90i3hf993.png)
Now, we an use the property
![\sqrt[]{a}*\sqrt[]{b}=\sqrt[]{a* b}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/n50x606xuwno4viaysc5.png)
to simplify it further:
![\begin{gathered} 36(\sqrt[]{2}*\sqrt[]{6}) \\ =36(\sqrt[]{2*6}) \\ =36\sqrt[]{12} \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/khgvu403tcndfo4acxeb.png)
We can break apart the square root using the property:
![\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/5b8qzraem6mwhdmx2wyn.png)
So, we have:
![\begin{gathered} 36\sqrt[]{12} \\ =36\sqrt[]{2}\sqrt[]{2}\sqrt[]{3} \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/hr1xzxu1g2y43wmuocof.png)
For the final simplification, we use the property,
![\sqrt[]{a}\sqrt[]{a}=a](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/rq4990r17qcp0e2816h7.png)
The final answer is:
![\begin{gathered} 36\sqrt[]{2}\sqrt[]{2}\sqrt[]{3} \\ =36(2)\sqrt[]{3} \\ =72\sqrt[]{3} \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/28eyhyqzbgzrd5adiirf.png)
Answer
![72\sqrt[]{3}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/7we68e4u9rgqfxhcrc0i.png)