What is the limit as n approaches infinity of \sqrt[n]{n^3} ?

The limit as n approaches infinity of \sqrt[n]{n^3} is 1

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limit as n approaches infinity of \sqrt[n]{n^3}

n \to \infty lim (n n^{3})

1

Solution steps

n \to \infty lim (n n^{3})

Apply exponent rules

= n \to \infty lim (e^{\frac{1}{n} l n (n^{3})})

Simplify

e^{\frac{1}{n} l n (n^{3})} : (n^{3})^{\frac{1}{n}}

= n \to \infty lim ((n^{3})^{\frac{1}{n}})

Apply exponent rules

= n \to \infty lim (e^{\frac{1}{n} l n (n^{3})})

Apply the Limit Chain Rule:

1

= 1

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What is the limit as n approaches infinity of \sqrt[n]{n^3} ?
The limit as n approaches infinity of \sqrt[n]{n^3} is 1