How to show that $\lim_{n\to\infty} c^n\sqrt n = 0$, where $c\in(0,1)$? 
How to show that $\lim_{n\to\infty} c^n\sqrt n = 0$, where $c\in(0,1)$? 

We often claim that exponent is "stronger" than root (and we even proved it last semester) but I can't remember how.

Hint: Write $a=\frac{1}{c}$. Then $a>1$. Let $a=1+x$. Using $(1+x)^n>nx$ and the Squeeze Theorem, you can get easily the limit.
