Question

Evaluate $\sqrt{11\sqrt{11\sqrt{11\sqrt{\mathrm{11.......}\infty }}}}$

Answer 1

Let,$y=\sqrt{11\sqrt{11\sqrt{11\sqrt{\mathrm{11.......}\infty }}}}$

$\Rightarrow y=\sqrt{11.y}$

$\Rightarrow y^2=11y$

$\Rightarrow y(y-11)=0$

$\Rightarrow y=0,11$

But $y$ cann't be $0$.

$\therefore y=11$