Which of the following statement is/are correct?

I. \(1728^{\frac{1}{3}} < 145^{\frac{1}{2}} < 1000^{\frac{1}{6}} \)

II. \(169^{\frac{1}{2}} < 2744^{\frac{1}{3}} < 343^{\frac{1}{3}} \)

III. \(2^{\frac{1}{2}} < 3^{\frac{1}{3}} < 6^{\frac{1}{6}} \)

1
Statement I and II
2
Statement I and III
3
Statement III and II
4
None

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