Which Is The Biggest?

Algebra Level 4

Find the largest value from the following:

12,23,34,45,56,\large \sqrt[2]{1},\sqrt[3]{2},\sqrt[4]{3},\sqrt[5]{4},\sqrt[6]{5},\ldots

If the largest value above is of the form nn+1\sqrt[n+1]{n}, give the value of n.n.

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