Answer
$x=5.6$
Work Step by Step
$\frac{x}{\sqrt {10}}=\frac{3\sqrt 2}{\sqrt 2+1}$
$\sqrt {10}*3\sqrt 2 = x*(\sqrt 2+1)$
$3\sqrt{20}=x*(\sqrt 2+1)$
$\frac{3\sqrt{20}}{\sqrt 2+1}=x$
$\frac{3\sqrt{20}}{\sqrt 2+1}*\frac{\sqrt2-1}{\sqrt2-1}=x$
$\frac{3\sqrt{40}-3\sqrt{20}}{\sqrt 2+1}*\frac{1}{\sqrt2-1}=x$
$\frac{3\sqrt{40}-3\sqrt{20}}{\sqrt 2*\sqrt2-\sqrt2+\sqrt2-1}=x$
$\frac{3\sqrt{40}-3\sqrt{20}}{2-1}=x$
$\frac{3\sqrt{40}-3\sqrt{20}}{1}=x$
$3\sqrt{40}-3\sqrt{20}=x$
$3(\sqrt{40}-\sqrt{20})=x$
$3(\sqrt{2*2*2*5}-\sqrt{2*2*5})=x$
$3(2\sqrt{2*5}-2\sqrt{5})=x$
$6(\sqrt{10}-\sqrt{5})=x$
$6*(3.162-2.236)=x$
$6*.926 = x =5.556$
