Question

The value of $\sqrt{5\sqrt{5\sqrt{\mathrm{5...}}}}$ is

• A. 1
• B. 2.5
• C. 5
• D. 25

Answer 1

The correct option is C 5

Let $\sqrt{5\sqrt{5\sqrt{\mathrm{5...}}}}$
$\Rightarrow x=\sqrt{5x}$

$\Rightarrow x^2=5x$
$\Rightarrow x^2-5x=0$

$\Rightarrow x(x-5)=0$
$\Rightarrow x=0$ or $5$
Neglecting $x=0$, then $x=5$.