a

$ \text{ Force on Q due to charge q is } F_1 = \frac{kqQ}{a^2}$

$\text { a is length of side of square }$

$ \text{Force due to charges q on Q are perpendicular so resultant of two are }$

$F_{1R} = \frac{kqQ\sqrt 2}{a^2}$

$\text{Force due to charge Q } F_2 = \frac{KQ^2}{2a^2} $

$\text{Since resultant force is zero } F_{net} = 0$

$ \Rightarrow  \frac{kqQ\sqrt 2}{a^2} + \frac{KQ^2}{2a^2} =0$

$\Rightarrow q = -\frac{Q}{2\sqrt 2}$

$\Rightarrow \frac{Q}{q} = -2\sqrt 2$