[tex]\begin{gathered}\\\implies\quad \sf \frac{(4+2\sqrt{3})(4-2\sqrt{3})}{\sqrt{11}}\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{(4^2-(2\sqrt{3})^2)}{\sqrt{11}}\quad((a+b)(a-b)=a^2-b^2)\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{(4^2-(2\sqrt{3})^2)}{\sqrt{11}}\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{16-(2^2\times(\sqrt{3})^2)}{\sqrt{11}}\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{16-(4\times3)}{\sqrt{11}}\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{(16-12)}{\sqrt{11}}\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{4}{\sqrt{11}}\\\end{gathered} [/tex]
Rationalising the denominator -
[tex]\begin{gathered}\\\implies\quad \sf \frac{4(\sqrt{11})}{\sqrt{11}(\sqrt{11})}\\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{4(\sqrt{11})}{11}\\\end{gathered} [/tex]
Required Answer :-
[tex]\quad\green{ \underline { \boxed{ \sf{ \sf \frac{4\sqrt{11}}{11}}}}}[/tex]
