Simplify a expression with nested radical signs Simplify :
$\sqrt{10+6 \sqrt{2}+5 \sqrt{3}+4 \sqrt{6}}$
I have tried completing square but failed, Can anyone help me please? Thanks.

$$10+6 \sqrt{2}+5 \sqrt{3}+4 \sqrt{6}=5(2+\sqrt3)+2\sqrt6(2+\sqrt3)=(2+\sqrt3)(5+2\sqrt6)$$
Now, $$5+2\sqrt6=3+2+2\cdot\sqrt2\cdot\sqrt3=(\sqrt3+\sqrt2)^2$$
and $$2+\sqrt3=\frac{4+2\sqrt3}2=\frac{3+1+2\cdot\sqrt3\cdot1}2=\frac{(\sqrt3+1)^2}2$$
Can you take it from here?
