RRB Paramedical Staff Nurse Model Paper 2

To find the greatest number from the given set of numbers. We calculate the LCM of radicals or powers of the different numbers to make the denominator of the powers same. Then, we can easily find the required order
Given numbers are $\sqrt{2},\sqrt[4]{3},\sqrt[6]{6}$
Taking LCM of 2,4 and $6=12$
Now, $\sqrt{2}={\left(2\right)}^{\frac{1}{2}}={\left(2\right)}^{\frac{6}{12}}$
$=\sqrt[6]{2^6}=\sqrt[12]{64}$
$\sqrt[4]{3}={\left(3\right)}^{\frac{1}{4}}={\left(3\right)}^{\frac{3}{12}}$
$=\sqrt[12]{3^3}=\sqrt[12]{27}$
$\sqrt[6]{6}={\left(6\right)}^{\frac{1}{6}}={\left(6\right)}^{\frac{2}{12}}$
$=\sqrt[12]{6^2}=\sqrt[12]{36}$
So, neither I nor II is correct