A.M of two surds is $5+9\sqrt{2}$, one of the surds is $1+12\sqrt{2}$ then square root of the second surd is

A.M of two surds is $5+9\sqrt{2}$
the surds are  $1+12\sqrt{2},x$
$\begin{array}{l}\frac{1+12\sqrt{2}+x}{2}=5+9\sqrt{2}\\ 1+12\sqrt{2}+x=10+18\sqrt{2}\\ x=9+6\sqrt{2}\end{array}$
square root of x is
$\begin{array}{l}=\sqrt{9+6\sqrt{2}}\\ =\sqrt{(\sqrt{6}{)}^2+(\sqrt{3}{)}^2+2\cdot \sqrt{3}\cdot \sqrt{6}}\\ =\sqrt{(\sqrt{6}+\sqrt{3}{)}^2}\\ =\sqrt{6}+\sqrt{3}\end{array}$