we need to find value of $$sqrt{6+sqrt{6+sqrt{6+...}}}$$ let $$sqrt{6+sqrt{6+sqrt{6+...}}}$$ = x here x = $$sqrt{6+x}$$ on squaring both sides $$x^2 - x - 6$$ = 0 x = 3 , x = -2 here -2 will be rejected as square root can not give negative value and hence x = 3 $$sqrt{6+sqrt{6+sqrt{6+...}}}$$ = 3