To solve the exercise first, rewrite √6
[tex]\sqrt[]{6}=\sqrt[]{2\cdot3}[/tex]Now, apply this law of radicals
[tex]\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}[/tex]Then, you have
[tex]5\sqrt[]{2}\cdot9\sqrt[]{6}=5\sqrt[]{2}\cdot9\sqrt[]{2}\cdot\sqrt[]{3}[/tex]Now, apply this law of radicals
[tex]\begin{gathered} \sqrt[]{a}\cdot\sqrt[]{a}=a \\ \text{ Then} \\ \sqrt[]{2}\cdot\sqrt[]{2}=2 \end{gathered}[/tex]Finally, you have
[tex]\begin{gathered} 5\sqrt[]{2}\cdot9\sqrt[]{6}=5\sqrt[]{2}\cdot9\sqrt[]{2}\cdot\sqrt[]{3} \\ 5\sqrt[]{2}\cdot9\sqrt[]{6}=5\cdot9\cdot2\sqrt[]{3} \\ 5\sqrt[]{2}\cdot9\sqrt[]{6}=90\sqrt[]{3} \end{gathered}[/tex]Therefore, the simplified form of the given expression is
[tex]90\sqrt[]{3}[/tex]and the correct and answer is option D.
