The reaction is
HClO3(aq) <----> ClO3-(aq) + H+(aq).
Concentrations
Initial 1 0 0
Change -x +x +x
Equilibrium 1-x x x
Kc = [ClO3-] [ H+] / [HClO3] = x^2 / 1-x = 10
10 - 10x = x^2
x^2 + 10x - 10x = 0
On solving
x = 0.916 M
so equilibrium concentration of H+ = x = 0.916 M