Make it solvable

This is solvable if and only if $x$ has a perfect square factor. Proof:

$x = a + b + 2\sqrt{ab}$ so $ab$ must be a square. So if a has an odd powered factor then b has the same odd powered factor.

$\sqrt{a}$ simplifies to a number of form $d*\sqrt{c}$ , this implies $\sqrt{b}$ simplifies to $e*\sqrt{c}$ therefore

$\sqrt{x} = d*\sqrt{c} + e*\sqrt{c} = (d+e)*\sqrt{c}$

$x = (d+e)^{2}*c$

so $x$ has a perfect square factor.

Counting the number of integers to 1000 which have a square factor takes awhile but is trivial. There are $392$ of them.