Given the initial expression
[tex]\sqrt[]{11\cdot2-6}+5(4^2-9)[/tex]
Notice that it is equivalent to
[tex]\sqrt[]{11\cdot2-6}+5(4^2-9)=(11\cdot2-6)^{\frac{1}{2}}+5(4^2-9)[/tex]
Simplify as shown below
[tex]\begin{gathered} \sqrt[]{11\cdot2-6}+5(4^2-9) \\ =(11\cdot2-6)^{\frac{1}{2}}+5(4^2-9) \\ =(22-6)^{\frac{1}{2}}+5(16-9) \\ =(16)^{\frac{1}{2}}+5(7) \\ =4+35 \\ =39 \end{gathered}[/tex]
Therefore, the answer is 39
