Ta có : 

a.  $x^{2}-5=0$

<=> $x^{2}-(\sqrt{5})^{2}=0$

<=> $(x+\sqrt{5})(x-\sqrt{5})=0$

<=> $\left\{\begin{matrix}x+\sqrt{5}=0 & \\ x-\sqrt{5}=0 & \end{matrix}\right.$

<=>  $\left\{\begin{matrix}x=\sqrt{5}& \\ x=-\sqrt{5} & \end{matrix}\right.$

Vậy $S={-\sqrt{5},\sqrt{5}}$

b.  $x^{2}-2\sqrt{11}x+11=0$

<=>  $x^{2}-2.x.\sqrt{11}+(\sqrt{11})^{2}=0$

<=>  $(x-\sqrt{11})^{2}=0$

<=>  $x-\sqrt{11}=0$

<=>  $x=\sqrt{11}$

Vậy $S={\sqrt{11}}$ .