An ideal gas is found to obey the equation \(P^2V=\) constant along with the ideal gas equation (here, \(P =\) pressure and \(V =\) volume). If initial temperature and volume are \(T_0\) and \(V_0\) respectively and it expands to a volume \(3V_0,\) then what is the final temperature?
(a) \(\sqrt 3T_0 \)
(b) \(\sqrt 2T_0\)
(c) \(\frac{T_0}{\sqrt 3}\)
(d) \(\frac{T_0}{\sqrt 2}\)