Respuesta :
[tex]9\sqrt[]{3}[/tex]Explanation:[tex]3\surd12-\surd32+\surd27+2\surd8[/tex]
We check if the numbers in under square root can be broken down into numbers we can find the square root:
[tex]\begin{gathered} 12\text{ = 4}\times3 \\ 32\text{ = 2 }\times16 \\ 27\text{ = 3}\times9 \\ 8\text{ = 2}\times4 \end{gathered}[/tex][tex]\begin{gathered} 3\surd(4\times3)-\surd(2\times16)+\surd(3\times9)+2\surd(2\times4) \\ 3\times\surd(4\times3)-\surd(2\times16)+\surd(3\times9)+2\times\surd(2\times4) \\ 3\times2\sqrt[]{3}\text{ - 4}\sqrt[]{2}\text{ + 3}\sqrt[]{3}\text{ + 2}\times2\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} 6\sqrt[]{3}\text{ -4}\sqrt[]{2}\text{ + 3}\sqrt[]{3}\text{ + 4}\sqrt[]{2} \\ 9\sqrt[]{3}\text{ -4}\sqrt[]{2}\text{ +4}\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} =\text{ 9}\sqrt[]{3}\text{ + 0} \\ =\text{ 9}\sqrt[]{3} \end{gathered}[/tex]