Does there exists $x\in\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ of the form $$ x=a+b\sqrt{2}+c\sqrt{3}+d\sqrt{5}+e\sqrt{6}+f\sqrt{10}+g\sqrt{15}+h\sqrt{30},\tag{1} $$ where $a,b,c,d,e,f,g,h\in\mathbb{Q}$, such that $$ x^2 = p+q\sqrt{30}, \qquad p,q\in\mathbb{Q},\tag{2} $$ but with one restriction: at least three of values $a,b,c,d,e,f,g,h$ are non-zero?
There are quite obvious $x$-solutions for one and two terms in $(1)$:
$(\sqrt{5})^2=5+0\sqrt{30}$,
$(1+\sqrt{30})^2=31+2\sqrt{30}$,
$(\sqrt{3}+\sqrt{10})^2=13+2\sqrt{30}$,
but how about three and more terms?