Consider the following in respect of the numbers \( \Large \sqrt{2}, \sqrt[3]{3} \) and \( \Large \sqrt[6]{6} \)
I. \( \Large \sqrt[6]{6} \) is the greatest number.
II. \( \Large \sqrt{2} \) is the smallest number.
Which of the above statements is/are correct?

\( \Large  \sqrt{2}, \sqrt[3]{3}, \sqrt[6]{6} \)

Taking LCM of 2, 3 and 6 = 12

Now, \(  \Large \sqrt{2} = \left(2\right)^{\frac{1}{2}} = \left(2\right)^{\frac{6}{12}} = \sqrt[12]{2^{6}} = \sqrt[12]{64} \)

\( \Large  \sqrt[3]{3} = \left(3\right)^{\frac{1}{3}} = \left(3\right)^{\frac{4}{12}} = \sqrt[12]{3^{4}} = \sqrt[12]{81} \)

\( \Large  \sqrt[6]{6} = \left(6\right)^{\frac{1}{6}} = \left(6\right)^{\frac{2}{12}} = \sqrt[12]{6^{2}} = \sqrt[12]{36} \)

So, neither I nor II are correct.