$R _{2} \rightarrow R _{1}+ R _{3}-2 R _{2}$

$\Rightarrow\left|\begin{array}{ccc}3 & 4 \sqrt{2} & x \\ 0 & k-6 \sqrt{2} & 0 \\ 5 & k & z\end{array}\right|=0$

$\Rightarrow(k-6 \sqrt{2})(3 z-5 x)=0$

if $3 z-5 x=0 \Rightarrow 3(x+2 d)-5 x=0$

$\Rightarrow x=3 d$ (Not possible)

$\Rightarrow k =6 \sqrt{2} \quad \Rightarrow k ^{2}=72$