# Find $\mathop {\lim }\limits_{n \to \infty } \sqrt[n]{{{3^n} + {5^n}}}$ [duplicate]

Find the limit $$\mathop {\lim }\limits_{n \to \infty } \sqrt[n]{{{3^n} + {5^n}}}.$$

Thanks.

-

## marked as duplicate by mrf, Nick Peterson, Hagen von Eitzen, Hanul Jeon, Thomas AndrewsJul 24 '13 at 6:29

What is bigger: $3$ or $5$? Think about it. – Cortizol Jun 25 '13 at 9:15

We have $$\lim_{n\rightarrow \infty}\sqrt[n]{{{3^n} + {5^n}}}=5\times\lim_{n\rightarrow \infty}\left[1+\left(\frac{3}{5}\right)^n\right]^{\frac{1}{n}}= 5.$$