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

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

Thanks.

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

What have you tried? –  ᴊ ᴀ s ᴏ ɴ Jun 25 '13 at 9:08
What is bigger: $3$ or $5$? Think about it. –  Cortizol Jun 25 '13 at 9:15

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