Answer
Let the charge Q at bottom left corner be considered, it is ready to move under repulsion
f1 = F(top, bottom) = kQ^2/L^2 [south] = x
f2=F(right, bottom) = kQ^2/L^2 [west] = x
f3 = F(diagonal, bottom) = kQ^2/[L root2]^2 [south-west]
f3 = x/2
—————————————–
resolve f3 along south & west
F(net south) = x + [x/2] cos 45 = x[1+ 1/2root2]
F(net south) = x[1+2root2] /2root2 = F
F(net west) = x[1+2root2] /2root2 =F
F(resultant) = sqrt[F^2 + F^2] = F root2
F(resultant) = [ x[1+2root2] /2root2 ][root2]
F(resultant) = x[1+2root2] /2
F(resultant) = kQ^2[1+2root2] /2L^2
thats it!!